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LOGIC 



OR THE 
ANALYTIC OF EXPLICIT REASONING 



BY 

GEORGE H. SMITH 

A CRITICAL 

HISTORY OF MODERN ENGLISH JURISPRUDENCE," " THEORY 
OF THE STATE," AND OTHER WORKS 



G. P. PUTNAM^S SONS 

NEW YORK AND LONDON 

Zbc Iknichcvbochct press 

1901 






THE LIBRARY QF 
CONGRESS, 

Two Copies ReceivfO 

MAY. 7 1901 

COPYWGHT CNTRV 

^ASS <^XXo. H9 
COPY A. 



Copyright, 1901 

BY 

GEORGE H. SMITH 



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PREFACE 



IT IS well known to those conversant with 
the current literature of Logic that recent 
logical theories diverge widely from the old 
Logic of Aristotle and the Schoolmen, and no 
less widely from each other. From this it hap- 
pens that, under the common name of Logic, 
we have many doctrines essentially different 
from each other ; and the student who desires 
to enter upon the study of the subject is thus 
confronted with the preliminary problem of 
determining under what name the true Logic 
is to be found. Nor in this case can he expect 
much help from his instructors; who, like the 
rest of the logicians, are hopelessly at a loss. 
Whether he shall study Logic — whatever may 
be his wishes and his determination — must 
therefore be a matter for chance to determine. 
And, even should he be so lucky as to light 
on a place where something like Logic is 
taught, it will probably be taught in so muti- 
lated a form and so mingled with extraneous, 
and even inconsistent matter, that it will be 



111 



iv PREFACE 

impossible for him to understand it or to ap- 
preciate its utility. Hence, if the plain truth 
is to be told, Logic, in the true sense of the 
term, is no longer taught or learned anywhere; 
but has become a lost art. 

But while the logicians of the day are thus 
at variance among themselves, there is un- 
fortunately one point in which they agree 
with each other, and also with Whately and 
others of the older logicians. This consists in 
the opinion that Logic is a purely formal 
science, and as such concerned only with the 
forms, and not with the matter or content of 
language or of thought; or, in other words, 
that it does not deal with what is thought or 
expressed, but with the forms of the thought 
or expression only. From this it must follow — 
if the view be accepted — that Logic, except 
merely as an improving mental exercise, can 
be of no practical utility; and this indeed is 
commonly asserted and always implied in the 
Logics of the day; which, though essentially 
different in other respects, agree in this. And 
from this again it must follow — as on this view 
was irresistibly argued by Locke, Stewart, 
Reid, and others — that the subject is unworthy 
of the serious attention of rational men ; which, 
on the premises assumed, has indeed come to 
be the verdict of the common sense of man- 
kind. Thus the student is discouraged from 



PREFA CE V 

the study of the subject not only by the con- 
fusion reigning over it and the almost insur- 
mountable initial difficulty of recognizing the 
true Logic among so many pretenders, but 
by the conviction impressed upon him by an 
irresistible argument and by the practically 
unanimous teachings of logicians, that Logic 
cannot be put to any practical use. 

The view taken of Logic in this work is dif- 
ferent. It is what I conceive to be the ancient 
and orthodox view, that Logic has to deal with 
the matter as with the forms of thought and its 
expression ; that it embraces in its scope every- 
thing that touches the right use of words, as 
instruments of reasoning, or, in other words, 
the whole subject of explicit reasoning or ratio- 
cination ; that it is the science fundamental to 
all others and essential to all who, in the search 
after truth, would pass beyond the mere evi- 
dence of their senses; that, in its educational 
aspect, it is not only an essential part, but the 
very foundation of rational education; and 
finally that, in use, it is indispensable to the 
rectitude of thought and of life. Hence, of 
all branches of learning, I believe it to be of 
the largest practical utility to man, and that 
all the learning of the day cannot compen- 
sate for its loss; and also that its decadence 
in modern times has been one of the great 
calamities of mankind. All this I attempt to 



VI PREFA CE 

establish and to illustrate practically in the 
following pages; to which I must refer for 
the complete proofs; but perhaps something 
towards this end may be effected in advance 
by explaining briefly how the work came to be 
written. 

In the investigation of Jurisprudence, Poli- 
tics, and Morality generally — to which my 
studies have been principally devoted — two 
important facts were forced on my attention, 
that seem to establish my present thesis: 

(i) The first of these was that the prevailing 
errors in the theory of Politics, Sociology, and 
Morality, and the Moral Sciences, or Science 
of Human Nature, generally, have their 
sources, almost always, in merely logical fal- 
lacies, and may be readily refuted by the ap- 
plication of familiar logical principles; all of 
which will be practically illustrated in treating 
of the fallacies. Here, then, I think, we have 
a practical proof of the indispensable utility 
of Logic, and the consequent refutation of the 
error that it deals only with the forms of 
thought or expression. For it is known to all 
logicians that the most serious and pernicious 
of the recognized fallacies are those that relate 
to the matter expressed in language, and are 
therefore called the material fallacies; which 
by logicians generally are admitted into Logic, 
but, as it were, on sufferance only. 



PREFACE VI i 

(2) The second fact I learned was that, 
though it is impracticable to refute such errors 
otherwise than by the application of logical 
principles, yet owing to the logical decadence 
of the age, and the general disuse of Logic, 
this mode of refutation is unavailable. Hence 
under existing conditions, there is no practical 
means of stemming the tide of moral and politi- 
cal heresy with which, with increasing violence, 
mankind is being afflicted ; and from this it 
follows, as a necessary inference, that the first 
step towards reform of doctrine, or life, in any 
direction, must be a revival of the study and 
use of Logic. My, work therefore is the result 
of a profound realization of this practical neces- 
sity, and of the imperative demand thus result- 
ing. Nor — however interesting the theory of 
Logic may have been to me — have I ever lost 
sight of what I conceive to be the most import- 
ant aspect of the subject, namely, its supreme 
practical utility. 

Generally, the object of the work is to vindi- 
cate, as against modern innovations, the old or 
traditional Logic. This constitutes a perfectly 
definite body of doctrine, rivalling in accuracy 
and in demonstrative force the Geometry of 
Euclid. Nor are there wanting treatises in 
which its theory and application are, on the 
whole, well explained, — as, e. g., notably 
Whately^s work; which, notwithstanding some 



VIU PREFACE 

manifest defects, still remains, not only the 
best, but the only elementary exposition of 
Logic, in the English language, that can be 
recommended to the student. But there are 
many reasons why a mere reproduction of the 
older works would be inadequate for our present 
occasions, to some of which I will briefly ad- 
vert. 

The first of these relates to the error, already 
considered, that prevailed with many of the 
old logicians, as with the new, that Logic is 
concerned only with the forms, and not with 
the matter of thought, or its expression. For, 
though this defect was supplied by the old 
logicians, — at the expense of their consistency, 
— by their admirable exposition of the doctrines 
of Definition and of Classification and Division 
and of the Term generally, and of the Material 
or so-called Non-logical Fallacies, yet their 
theory of Logic remained incomplete, and 
Logic was thus mutilated of some of its most 
vital parts. 

Again, the searching investigation to which 
the old Logic has been subjected by modern 
logicians, though its general effect has been to 
vindicate its substantial truth and to re-estab- 
lish it on a broader and firmer basis, has yet 
resulted in several additions to logical doctrine, 
to which it is essential that the attention of the 
student should be directed. Hence, while one 



PREFACE IX 

of the principal objects of this work is to vindi- 
cate the truth and the supreme utility of Logic 
as anciently conceived, it is also contemplated 
to supply the radical defect I have alluded to, 
and, at the same time, to incorporate with the 
old Logic the approved results of modern re- 
search ; some of which are of great importance. 
It remains to add a few words as to the 
method and style with which the subject of 
the work is treated. Logic is admittedly a 
demonstrative or apodictic doctrine, and should 
therefore be treated by the method appropriate 
to subjects of that nature. This consists in the 
accurate formulation of our premises, and in 
reasoning rigorously from them, as in geome- 
try. But this method demands the use of 
a style altogether different from that in com- 
mon use; which may be called the popular or 
rhetorical. For it is the peculiar characteristic 
of the logical style that it must be accurate or 
aphoristic, /. ^., that it must express the exact 
truth without any admixture of error. For 
the same truth holds good in ratiocination, as 
in nature generally, that hybrids are unprolific; 
and hence the slightest admixture of error in 
our premises will render them altogether use- 
less for logical inference. Our method will 
therefore demand the exact analysis of the 
terms we use and the formal statement of our 
propositions; which to the general reader is 



X PREFA CE 

distasteful. For while the logical style ad- 
mits, and even requires, great brevity of .ex- 
pression, — so that, in general, volumes of 
ordinary disquisition may, by means of it, be 
compressed into a brief space, — yet it demands 
a degree of attention and independent thought 
that only a few highly trained or exceptionally 
gifted minds are willing to give, or perhaps 
without great exertion are capable of giving. 
But this is nevertheless essential to the fruitful 
study of Logic, as of apodictic science gener- 
ally. There is no royal road to Logic any 
more than to Geometry 

The best type of this style is found in the 
Mathematics, and especially in the writings of 
Euclid and the geometers, whose style and 
method I have sought to emulate, — with what 
success remains to be judged. I trust, how- 
ever, I may, without vanity, say of the result, 
with Hobbes, that while '* there is nothing I 
distrust more than my elocution, nevertheless 
I am confident, excepting the mischances of 
the press, it is not obscure/' 

George H. Smith. 

Los Angeles, February 26, 1900. 



CONTENTS 



PAGE 



Introduction — Of the Function of 

Logic i 

BOOK I 

THE ANALYTIC OF RIGHT REASONING 



CHAPTER I 
Rudimentary Notions 

CHAPTER II 

Doctrine of the Term 

I — Of the Nature of the Term 
II—Of the Several Kinds of Terms 
III — Of the Analysis of Terms 

chapter III 

Doctrine of the Proposition . 

I — Rudiments of the Doctrine . 
II— Several Theories of Predication 
III— Of the Predicables 
IV — Of the Relations between Terms 



23 



zz 

40 

44 



SI 

51 

55 
61 

64 



XI 



Xll CONTENTS 

CHAPTER IV 

PAGE 

Doctrine of the Syllogism . . -74 

I — Rudiments of the Doctrine ... 74 

II — The Principle of Substitution . . 77 

III — Of Mathematical Reasoning ... 85 

CHAPTER V 

Summary of the Traditional Logic . 91 

I — Of the Traditional Logic Generally . 91 

II — The Traditional Doctrine of the Prop- 
osition ...... 92 

III— The Traditional Doctrine of the Syl- 
logism ; . . . . .104 

BOOK II 
APPLIED LOGIC 

PART I 
OF THE METHOD OF LOGIC 

CHAPTER VI 

Of the Logical Processes . • •123 

CHAPTER VII 

The Rules of Logic .... . 137 

I — Of the Rules of Logic Generally . 137 

II — Rules of Judgment .... 142 

III— Rules of Inference . . . . 145 



CONTENTS Xlll 

PART II 
DOCTRINE OF THE FALLACIES 

CHAPTER VIII 

PAGE 

Definition and Classification of Fal- 
lacies 149 

CHAPTER IX 
Fallacy of Non-Significance, or Non- 
sense 157 

CHAPTER X 
Fallacy of False Definition . . . 168 

CHAPTER XI 
Illicit Assumption of Premises {Fetitio 

Principit) 175 

CHAPTER XII 
Mistaking the Issue and Irrelevant 

Conclusion {Ignoratio Elenchi) . .188 

CHAPTER XIII 
Illicit Conversions 198 

CHAPTER XIV 
Illicit Substitutions of Terms . . 200 

CHAPTER XV 

Equivocation 203 

CHAPTER XVI 
The Traditional Doctrine of Fallacies. 210 

I — Aristotle's Classification OF Fallacies . 210 

II — Fallacies m Z>/<:/2W^ (Equivocation) . . 214 

III — 0^i:YiY.Yk\A.kC\^^ extra Dictionem . .219 



LOGIC, OR THE ANALYTIC OF 
EXPLICIT REASONING 



INTRODUCTION 



OF THE FUNCTION OF LOGIC 

§ I. The Theory of Knowledge, a De- 
partment OF THE Theory of Opinion. 
— The problem of the origin and nature of 
knowledge has occupied the attention of the 
philosophers for something over twenty-five 
centuries without much progress toward solu- 
tion. This perhaps results from the fact that 
the problem itself is but part of a larger prob- 
lem that should be first considered ; for know- 
ledge is but a species of opinion, which may be 
either true or false. Hence the inquiry as to 
the origin and nature of opinion must be the 
first in order of investigation. Nor until this 
investigation has been made will we be pre- 
pared to determine the specific characteristics 



2 LOGIC 

by which true knowledge is differentiated from 
opinion in general. 

§ 2. Knowledge but Verified Opinion. 
— Men generally confound this distinction, and 
regard all their settled opinions or beliefs as 
knowledge. This is not merely false, but ab- 
surd ; for not only do the opinions of men 
differ, but the opinions of the same man are 
often inconsistent and contradictory ; and 
some, it is clear, must be false. And this is 
apparent also from the nature and generation 
of our opinions. For, in general, these come 
to us not from any conscious process, but 
naturally and spontaneously and from many 
sources, as, e, g,, from testimony, from author- 
ity, from inaccurate observation or careless 
reasoning, and even largely from mere pre- 
judice or bias. Hence, familiar to us as our 
opinions are, their origin in general is as un- 
known to us as were anciently the sources of 
the Nile; nor have we any just notion of the 
grounds on which they rest, or of the nature 
and justice of their demands on our belief. 
Hence, until some means of verifying our 
opinions be found and applied, we can have 
no assurance of their rectitude. The first step 
in Science or Philosophy must, therefore, be 
to distinguish between verified and unverified 
opinions. The former constitutes true know- 
ledge or science; the latter — though it is in 



INTRODUCTION 3 

fact the stuff out of which most of the current 
philosophy is woven — has no just pretension 
to the name. 

§ 3. The Sources of Opinion Distin- 
guished. — With regard to the source of our 
opinions, we must distinguish between those 
derived from our own experience and those de- 
rived from the experience of others ; of which 
those derived from the common experience of 
mankind are the most extensive and important. 
The last have come to us by means of lan- 
guage, which may therefore be said to be 
their source; nor could they otherwise have 
been transmitted to us. The former constitute 
— comparatively speaking — but a small and in- 
significant part of the sources of the mass of 
our opinions. For the greater part of what 
we know, or think we know, is not original 
with us, but has come to us from others by or 
from language. The distinction, therefore, is, 
not between opinions derived from experience 
and opinions not so derived, — for it may be 
said all opinions that are true, or rather that we 
know to be true, are derived ultimately from 
experience,^ — but in the manner of their deri- 
vation ; the one class being those opinions de- 
rived by us, each from his own experience, the 
other, those derived not directly from our own, 

* The distinction made in the text is of fundamental import- 
ance. The necessity of a constant resort to experience as the 



4 LOGIC 

but from the experience of others from or 
through language. 

§ 4, Of Language as a Record of 
Human Thought. — Of the two classes of 
opinions, the latter is infinitely the more ex- 
tensive in scope and important in character; 
for all that men have seen or thought or felt 
has been expressed, and is thus preserved to 
us in language; which thus constitutes, as it 
were, the record of the results of all human 
experience and reason. Here, therefore, is to 
be found the principal source of our opinions, 
verified and unverified — that is to say, not 
only of our opinions generally, but of our 
knowledge or science. But, regarding Ian-, 
guage as a record and source of opinion, we 
must distinguish between the forms in which 
opinion is embodied in it. These forms may 
be described, with sufficient accuracy for our 
purposes, as consisting in terms, propositions, 
and syllogisms. But of these the syllogism in 
its end and effect is but the reduction of two 

ultimate source of our knowledge cannot be too strongly in- 
sisted upon. But to construe this proposition as referring to 
each man's individual experience is to fall into an error of the 
kind called by Bacon *' Idols of the Den" ; and thus to fall 
under the reproach of Heraclitus " that men search for know- 
ledge in lesser worlds, and not in the greater or common 
world," i, e.^ the great world of the common notions of man- 
kind, derived from the universal experience and embodied iii 
the common language. {Nov, Org,, bk, i., aph. xliii.) 



IN TR OD UC TION 5 

propositions to one, and, in this connection, is 
of interest to us merely as exhibiting one of 
the modes in which opinion is formed. It will 
be sufficient, therefore, to distinguish the term 
and the proposition as- the two forms in which 
opinions, or the elements of opinions, are em- 
bodied. But the proposition is itself of two 
kinds, differing essentially in nature. In the 
one — if not an inference — it is simply the state- 
ment of a relation intuitively perceived to exist 
between two terms or names, that is to say, 
between the notions or concepts denoted by 
them, — as, e, g,^ where we say, '' Bodies are 
affected by gravity," or ** Two islands cannot 
be contiguous," or ** Fishes live in the sea,*' 
or ** Man is rational''; in the other, it is a 
statement of a relation between terms, not in- 
tuitively perceived — or logically inferred — but 
assumed to be true from testimony or other- 
wise, — as, e, g,, where we say, *' Brutus was 
one of the murderers of Csesar," or '* Hannibal 
was conquered by the Romans.'' The former 
— in accordance with the definitions used 
throughout this work — will be called a judg- 
ment ; tliQ Isitter, slw assumJ>tio7i, In the former 
case the truth of the proposition is involved in 
the meanings of the terms, — z, e., in the nature 
of the concepts or notions denoted by them ; 
and this is true also of all iiiferences, or propo- 
sitions inferred from judgments. So that with 



6 LOGIC 

relation to all such propositions, whether in- 
tuitively perceived or inferred, the original 
sources of opinion are the notions or concepts 
in which they are involved. We may therefore 
distinguish, as the two sources of opinion af- 
forded us by language, (i) the notions or con- 
cepts expressed in terms, and (2) assttmptionSy 
or assumed propositions. 

With the truth of the latter, or the evidence 
on which they rest for credence, Logic is not 
concerned ; nor is it concerned with them in 
any way, except as premises from which to 
argue; or to reject them as such, if they can be 
shown by logical processes to be false. But 
where such propositions are justified by experi- 
ence, and come thus to be generally received, 
the result universally, or almost universally, is 
the generation of a new notion, — i. e.y the 
notion of the relation perceived between its 
terms; which is either expressed in a new term 
or added to the content or meaning of an exist- 
ing term; and this, indeed, to the extent it is 
attainable, is the end of science, and, in a per- 
fect language, — were such attainable, — would 
be the general result. Thus the general pro- 
gress of human thought consists largely in the 
conversion of propositions into terms or names 
denoting the relations expressed in them ; and 
hence, generally, in terms are contained many 
propositions, as, e, g,y in '* gravity," ** justice," 



INTRODUCTION / 

etc. — in the former of which is contained a large 
part of Physical Science, and in the latter nearly 
the whole theory of the State. In this way the 
stock of the common notions of mankind is 
continuously accumulated, until it may be said 
that the great part of all that has been achieved 
in thought by men is expressed or implied in 
terms or names. Here, therefore, are to be 
found the principal sources of opinion; and, 
compared with these, opinions embodied in 
propositions that cannot be, or have not been, 
reduced to single notions are limited in ex- 
tent, and of secondary importance. And this 
is especially true with regard to the Moral 
Sciences; under which name I include all the 
various branches of the science of human 
nature; for in these sciences it is impossible 
to conceive of any rudimentary notion or 
thought that has not, in the long history of 
man, been conceived by the human mind and 
embodied in terms. With reference, therefore, 
to all that has been achieved in science or in 
popular thought, the sources of all our opin- 
ions, verified and unverified, — that is to say, 
of all our knowledge or supposed knowledge, 
— are to be sought in language, and, prin- 
cipally, in the notions expressed in terms or 
or names ^ ; and consequently, with reference to 

^ If the reader will thoroughly apprehend this proposition, 
he will find in it the key, not only to Logic, but to all Phil- 



8 LOGIC 

knowledge or supposed knowledge of this kind, 
our method must consist in the study of lan- 
guage. 

§ 5. Received Opinion Distinguished 
fromTrue Knowledge. — Our opinions, how- 
ever, are derived from this source in two ways, 
which must be distinguished : namely, by tradi- 
tion, — by which our opinions are delivered to 
us ready made in the form of propositions, — 
and by reasoning upon the notions embodied 
in terms. For the thought contained in lan- 
guage is embodied in two ways, namely, 
explicitly, in the form of propositions, and 
implicitly y in terms; and of propositions, — as 
we have seen, — many are but explicit state- 
ments of what is implied in the notions 

osophy. The elements of knowledge, so far as already 
achieved, we repeat, are the notions or concepts incarnate in 
terms ; and these must always constitute the principal source 
of our knowledge ; for, in comparison with the knowledge 
thus expressed or implied, the original contributions of the 
most gifted of men to the common stock must be inconsider- 
able. Nor can any such contribution to the knowledge of 
mankind be regarded as completely achieved until embodied 
in definite terms ; and hence the formation of such terms, or, 
what is the same, of the notions embodied in them, must be 
regarded as the end of scientific discovery. There is, there- 
fore, nothing paradoxical in the assertion of Condillac that 
** Science is but language well made." Hence, to repeat what 
has been said, it is to the common stock of notions thus gradu- 
ally accumulated by mankind and permanently secured by ex- 
pression in terms, that we must resort as the principal source 
of all knowledge or science. See Appendix A. 



IN TR OD UC TION 9 

expressed in terms, as, e, g,, in the prop- 
osition, ** All bodies are affected by grav- 
ity," etc. With reference to these, though 
they may be true, their mere reception cannot 
be said to constitute knowledge; but — in the 
proper sense of the terms — we can know them 
only when we have reasoned them out for our- 
selves from the primary notions in which they 
are involved; as, e, g,, in the Mathematics, 
where we cannot be said to have mastered a 
theorem until we are able to work it out from 
the premises by the exertion of our own powers 
unassisted by memory. With reference to all 
that has been achieved in thought, therefore, 
our method in the pursuit of knowledge must 
begin with the apprehension of the notions 
already formed by men and embodied in terms; 
and this involves the testing of those notions 
for ourselves by comparing them with the 
realities to which they are supposed to corre- 
spond. 

§ 6. The Physical and Mathematical, 
Distinguished from the Moral Sciences. 
— These observations apply equally to the 
Physical and Mathematical as to the Moral Sci- 
ences ; but there are differences, partly essential 
and partly accidental, between the two classes 
of sciences, which must be adverted to ^ : 

(i) In the Physical Sciences and in the 

^ See Appendix B. 



lO LOGIC 

Mathematics, technical terms expressing ac- 
curately the concepts or notions involved are 
exclusively used, but in the Moral Sciences it 
is otherwise ; for there the notions developed 
by the experience and reasoning of mankind — 
which must always constitute the principal 
source of our knowledge — are in general loosely 
and inaccurately expressed, and the same vocal 
sign, or vocable, is commonly used to denote 
many different notions more or less nearly re- 
lated ; nor, with reference to these, does the 
term in general express the notion accurately. 
Hence the necessity of definition, which is at 
once the fundamental and the most difficult 
of the logical processes. But in the Physical 
Sciences the notion is always accurately defined 
by the thing itself; and so in the Mathematics, 
though highly abstract, our notions are always 
clearly defined. Thus in these sciences the 
logical processes are so simple that it is impos- 
sible to err, unless by inadvertence, and all 
errors are quickly corrected ; and hence a tech- 
nical knowledge of Logic is but little needed.^ 
But in the Moral Sciences it is different, for 
here the difficulty of defining our terms is 

^ Hence, from disuse of the more difficult of the logical 
processes, a man in the former case, may be a competent 
naturalist without being much of a reasoning creature ; and 
in the latter, a great mathematician and yet a child in the 
practical affairs of life, individual and social. 



IN TROD UCTION 1 1 

great, and often insuperable, and hence, in the 
prosecution of these sciences. Logic must 
always be an indispensable instrument. 

(2) To a certain extent this difference be- 
tween the two classes of sciences is an essential 
one, and cannot be altogether removed. But 
to a large degree the Moral Sciences are sus- 
ceptible of apodictic treatment, and by such 
treatment may be indefinitely assimilated in 
nature to what are commonly called — though 
not exclusively entitled to the name — the 
Exact Sciences; for a large part of the Moral 
Sciences, including nearly all the fundamental 
principles upon which they rest, are purely 
apodictic. For, though it is commonly sup- 
posed there is an essential difference between 
Mathematical and what is called Moral Reason- 
ing, this is not true ; all ratiocination (not fal- 
lacious) is essentially of the same character and 
equally conclusive.* 

(3) Hence it may be observed as a corollary, 

'This is much insisted upon by Locke: "Confident I 
am," he says, "that if men would, in the same method, and 
with the same indifferency, search after moral, as they do after 
mathematical truths, they would find them to have a stronger 
connection, one with another, and a more necessary conse- 
quence from our clear and distinct ideas, and to come nearer 
a perfect demonstration than is commonly supposed " {Essay, 
bk. iv. , chap, iii., 20). "By what steps we are to proceed 
. . . is to be learned in the school of the mathematicians, 
who, from very plain and easy beginnings, by gentle degrees, 



12 LOGIC 

the principal task before us, with reference to 
the Moral Sciences, is to reduce them as far as 
possible to apodictic or scientific form. This, 
under present conditions, will still leave an im- 
mense field of investigation in which we must 
resort directly to experience, and especially to 
experience as embodied in history and statis- 
tics; but until all that is susceptible of being 
so reduced is reduced to scientific form, no 
progress can be made in dealing with matters 
depending upon experience. 

(4) With regard to the Physical Sciences 
another difference is to be noted, namely, 
between what has been achieved and the dis- 
covery of new facts; with reference to which 
the instrument of discovery is mainly experi- 
ment and observation, or, as it is commonly 
called, the Inductive Method. In this respect 
these differ from the Moral Sciences, where, 
though the same method must always be used, 
its function is confined chiefly to the process of 
definition.* 

and a continued chain of reasonings, proceed to the discovery 
and demonstration of truths that appear at first sight beyond 
human capacity " {Id., bk. iv., chap, xii., 7, 8). '* This gave 
me confidence to advance the conjecture which I suggest, 
Chap, iii., viz., that Morahty is capable of demonstration as 
well as Mathematics." 

^ The nature of Logic, and of the relation of the Inductive 
Method to Logic, is thus precisely expressed by Bacon : 

" The syllogism consists of propositions, propositions of 



in tr od uc tion 1 3 

§ 7. Of the Modes in which Opinion 
IS Generated. — With reference to results 
achieved and embodied in language, and to 
our opinions generally, the process by which 
our notions or concepts are derived is the re- 
verse of what is commonly supposed. In the 
discovery of new facts, or the formation of new 
concepts, we commence with the conception of 
the concrete, and, the concept being formed, 
we find the name. But this, in the develop- 
ment of thought at which we have arrived, can 
occur only in the Physical Sciences. For, as 
we have observed, it is hardly probable that 
in the Moral Sciences any rudimentary thought 
can ever occur that has not already occurred 
to some one and been expressed in language. 
Hence, with regard to all matters dealt with 
in the Moral Sciences (as also in the Physi-" 
cal Sciences with regard to results already 
achieved), the order of our cognitions is, first, 
to learn the woids, — i, e,, the word-signs or 

words, words are the signs of notions. If, therefore, the 
notions (which form the basis of the whole) be confused and 
carelessly abstracted from things, there is no solidity in the 
superstructure. Our only hope then is in genuine induction " 
{Nov, Org., bk. i., aph. xiv). 

The subject is more fully developed in aph. lix., and beauti- 
fully illustrated in aph. xcv. See also his doctrine of Idols, 
aph. xxxviii. et seq. It may be observed here, in passing, that 
no student of Philosophy, and still less of Logic, can afford to 
neglect the first book of the Novum Organum or the De 
A ugmentis. 



14 LOGIC 

vocables, — and afterwards, the concepts or 
notions expressed in them/ 

§ 8. Our Supposed Knowledge often 
Nonsense. — And as the latter function — out- 
side the Exact Sciences — is in general very 
lamely performed, the result is that the greater 
portion of our supposed knowledge in abstract 
matters consists of words without definite 
notions attached to them, and is therefore 
merely nonsense. For when we reason with 
undefined or ill-defined terms we are dealing 
with mere delusions or dreams — like Ixion 
embracing clouds and begetting monsters. 
Thus, e. g.^ when we assert, with Bentham and 
Austin, that General Utility is the ultimate 
test or principle by which the just and the un- 
just and right and wrong generally are to be 
determined, we are in fact talking nonsense; 
for it cannot be determined from this expres- 
sion whether we have in view the welfare of a 
mere majority, or two thirds, or three fourths, 
or other proportion of mankind, and hence 
from this premise all sorts of extravagant 
opinions are deduced. Hence the mass of us 

^ The logicians, from and including Hamilton, have en- 
tirely overlooked this distinction, and have thus substituted 
for the old logical doctrine of Simple Apprehension, the psy- 
chological doctrine of Conception, — a doctrine necessary to be 
understood, but vi^hich is concerned rather vi^ith the original 
formation of language than with its use as an instrument of 
reasoning. 



INTRODUCTION' 1 5 

generally, and all of us in many matters, — like 
Moliere's hero, who was surprised to find that 
he had been talking prose all his life, — have all 
our lives been' talking nonsense/ And this is 
true not only of opinions commonly regarded 
as nonsensical, but of all opinions involving 
either undefined notions or notions to which 
there are no corresponding realities. 

§ 9. The Critical Spirit Essential to 
Wisdom. — Our wisdom is therefore to be 
measured, not by the extent of our learning, 
or by knowledge of detached facts, or by vivac- 
ity of thought or expression, or by the confi- 
dence of our belief, but chiefly by the capacity 
to judge our supposed knowledge, and to de- 
tect its falsity or non-significance. In this way 
Socrates modestly explained the oracle of the 
Delphic god, that he was ** the wisest of man- 
kind.'' For, he said, he alone had discovered 
that all men were ignorant, including himself; 
but others mistook their ignorance for know- 
ledge.^ We conclude, therefore, as we began, 
that what we regard as our knowledge consists 
mainly of unverified opinions or beliefs, and 
that however firmly these may be established, 

^ See Appendix C. 

^ As explained by Grote (cited infra, § 16, App. H), the thesis 
of Socrates was that " the natural state of the human mind " 
is "not simply ignorance, but ignorance mistaking itself for 
knowledge." 



l6 LOGIC 

or however passionately they may be asserted 
and believed, they do not necessarily, or even 
generally, constitute true knowledge. Hence, 
until we are enabled to distinguish the true 
from the false, we can have no assurance of 
their rectitude or truth. 

§ lo. Logic the Ultimate Test or Cri- 
terion OF Truth. — We must, therefore, 
seek some tests or criterions — if any there be 
— by which the truth or falsity of our beliefs 
may be determined; and of such two only can 
be conceived ; namely, Experience and Reason- 
ing, or Logic. Of these the former is more or 
less efificiently used by men in general; and in 
concrete matters and in the ordinary familiar 
affairs of life, its operation is moderately satis- 
factory. For thus, by actual contact with the 
hard facts of our experience, our opinions or 
beliefs are, to a large extent effectually, and 
often painfully, modified and corrected. But 
the function of experience is simply to furnish 
Reason with materials on which to work; and 
of Reasoning, or Logic, as Hobbes says: ** So 
far are the mass of men from using it, that 
they do not even know what it is.'' ^ 

^ " The most part of men, though they have the use of rea- 
soning a little way, as in numbering to some degree, yet it 
serves them to little use in common life ; in vi^hich they gov- 
ern themselves, some better, some worse, according to their 
differences of experience, quickness of memory, and inclina- 
tion to several ends ; but especially according to good or evil 



INTRODUCTION 1 7 

§ II. The Decadence of the Age in 
Logic and the Moral Sciences. — And this 
is true not only of the common people, but of 
the educated, and even of the philosophers and 
the professors; who in the last century, owing 
to the disuse of Logic, have in fact lost the 
very idea of it; so that in our schools and 
universities, under the name of Logic, any- 
thing but Logic itself is taught, and it has thus 
become a lost art.' Yet, obviously, in all 
abstract matters, and especially in Morality, 
Politics, and all the different branches of the 
Science of Human Nature, experience, while 
useful to us, can go but a little way, and 
therefore Logic must be an indispensable in- 
strument. Hence it is to the disuse of Logic 
that the existing incoherent and chaotic state 
of the Moral Sciences is to be attributed.'^ It 
may therefore be confidently hoped that by the 
renewed use of Logic a revival of these sciences 
is to be anticipated, vying in extent with that 
of the concrete sciences in modern times, and 

fortune, and the errors of one another. For as for 'science,' 
or certain rules of their actions, they are so far from it that 
they know not what it is*' {lev., chap. v.). 

^ " We live in an age," says De Morgan, " in which formal 
logic has long been banished from education ; entirely we 
may say from the education of the habits." The proposition 
is even truer of the present day ; for in De Morgan's time 
there still survived some of the old style of logicians. 

2 See Appendix D. 



1 8 LOGIC 

far surpassing them in practical utility to the 
human race/ 

§ 12. Of Authority and Prejudice. — I 
would not, however, in thus explaining and 
commenting upon the general dominance of 
authority and prejudice over men, be under- 
stood as altogether condemning it. Under 
existing conditions, and perhaps under all con- 
ditions, the opinions of the masses of mankind, 
in Politics and other matters of common con- 
cern, must be determined mainly by custom and 
authority. Hence the distinction made by the 
old philosophers between their esoteric and ex- 
oteric doctrines ; the latter consisting of those 
that could be taught to the masses, the former, 
of those that required the peculiar training of 
the philosopher to comprehend — a profound 
distinction that has been lost in modern times. 
But though it may not be possible, or perhaps 
even desirable, to make all men philosophers, 
yet it is possible to make the masses of them 
logical in the matters with which they are con- 

^ The argument of Demosthenes in the first Philippic may 
be readily applied to the proposition asserted in the text : 
"First I say, you must not despond, Athenians, under your 
present circumstances, wretched as they are ; for that which is 
worst in them as regards the past is best for the future. 
What do I mean? That your affairs are amiss, men of 
Athens, because you do nothing that is needful ; if, not- 
withstanding you performed your duties, it were the same, 
there would be no hope of amendment." 



INTRODUCTION 1 9 

versant ^ ; and for those who aspire to be lead- 
ers of opinion, Logic is essential. For these, 
if worthy of the function to which they aspire, 
cannot afford to be deficient in this respect; 
they must either be logicians, or false prophets, 
or blind leaders of the blind. 

§ 13. Plan of the Work.— Though I re- 
gard the study of Logic as essential to the cul- 
tivation and the use of the reasoning powers, 
— and hence as indispensable to the Moral Sci- 
ences, — yet it is chiefly as a test or criterion of 
fallacy that I propose to treat it. This use of it 
will, of course, necessitate some consideration 
of the elementary principles and rules of Logic 
as necessary to the understanding of the Doc- 
trine of the Fallacies. But this part of my essay 
will be abbreviated to the utmost extent con- 
sistent with this object; that is to say, I will 
try to include everything essential to the under- 
standing of the rudiments of Logic, but noth- 
ing more. If I should fail in this, and anything 
necessary should be omitted, the defect may 
be readily obviated by reference to the work 
of Whately, who, among elementary writers, 
may be regarded (in any true sense of the 
word) as the last of the logicians. 

The subject will be treated in two books, the 
first entitled ** The Analytic of Right Reason- 
ing," the second, '* Applied Logic " ; the latter 

* See Appendix E. 



20 LOGIC 

of which will include two subjects, namely: 
'' The Method of Logic " and " The Doctrine 
of the Fallacies," or *' The Analytic of Wrong 
Reasoning/' In treating of the last, the ex- 
amples of the several fallacies will be taken 
almost exclusively from current theories of 
Politics and Morality. Our examples will 
therefore consist, not of mere trivialities, 
such as are so common in books on Logic, 
but of fallacies that, in perverting moral and 
political theory and in corrupting practice, 
have dominated, and still continue to domi- 
nate, the fortunes of mankind. They come 
to us, therefore, as veterans of what Hobbes 
calls the ** Kingdom of Darkness,'* crowned 
with the laurels of victory.^ 

^ Lev., chap. xliv. : see Appendix F. 




BOOK I 

THE ANALYTIC OF RIGHT 
REASONING 



21 



BOOK I 

THE ANALYTIC OF RIGHT 
REASONING 



CHAPTER I 



RUDIMENTARY NOTIONS 



§ 14. Definition of Logic and of In- 
volved Terms. — Logic is defined by Whately 
as the science and also the art of reasoning. 
Reasoning may be defined as consisting in the 
exercise of the comparative or discursive fac- 
ulty of the mind — that is to say, the faculty by 
which our notions or concepts are compared 
with each other, and with the realities to which 
they are supposed to correspond, and their re- 
lations with each other, and with such realities 
are perceived. Or we may define reason as 
the faculty, and reasoning as consisting in its 
exercise.* But Logic — by which I mean the 

^ The terms reason and reasoning, though conjugate, have 
unfortunately been divorced by logicians, and, following 

23 



24 LOGIC 

traditional Logic — is not to be regarded as 
having to deal with reasoning in general, but 
with explicit reasoning only, or ratiocination; 
which may be defined as reasoning expressed 
in language, or, so far expressed that the miss- 
ing parts are understood. Hence it is rightly 
said by Whately that Logic is exclusively con- 
versant with language; by which is meant, not 
merely the signs of thought, but also the 
thought signified/ This follows from the 
definition, and also from considering the sev- 
eral subjects of which it treats, which, by the 
universal consensus of logicians, consist of the 
Doctrines of the Term, of the Proposition, and 
of the Syllogism. But all these are simply 
parts or kinds of language. 

§ 15. Ratiocination Defined. — But Ra- 
tiocination, being a species of reasoning, must 
consist in the comparison of concepts or 
notions, and these, in order to fall within the 
province of Logic, must, ex vi termini^ be ex- 
pressed in terms. Hence, Ratiocination must 
be defined as consisting in the process of com- 

them, by lexicographers generally ; and accordingly Locke 
is blamed by Whately for confounding them. But in this 
Locke is right, and the logicians wrong ; and the usage of the 
latter has been the source of infinite confusion in Logic. As I 
use the terms, Reason includes the faculties of Inference, 
Judgment, and Simple Apprehension ; and Reasoning the 
corresponding processes. 
^ See Appendix G. 



RUDIMENTARY NOTIONS 25 

paring terms, with the view of perceiving their 
relations. And this necessarily implies, also, 
the process of determining the meaning of the 
terms compared, or, in other words, the process 
of definition. 

§ 16. Logic Defined. — Logic, regarded as 
a theory, may, therefore, be defined as the 
Analytic of Explicit Reasoning, or of Ratio- 
cination — meaning, by this expression, the 
systematized results of an analysis of the pro- 
cesses involved in ratiocination.^ And its 
practical end is to determine the meanings of 
terms and the relations between the concepts 
or notions denoted by them.^ 

§ 17. Of the Several Kinds of Terminal 
Relations. — The relations between terms are 
of two kinds, which may be called innnediate 
and inferred ; and the former, again, are of 
two kinds, that, for lack of better names, may 
be called intuitive and quasi-intuitive, 

§ 18. The Intuitive Relations of Terms. 
— Of the former kind are all those relations 
between terms that are intuitively perceived 
upon comparing them together, as, e, g,^ the 

^ See Appendix H. 

^ ** Knowledge [is] but the perception of the connection and 
agreement or disagreement or repugnancy of any of our ideas " 
(Locke, cited §110 n. g. App. N). *' Knowledge is not so 
much increased by a continued accession of new ideas as by 
perceiving the relations of those ideas which we have already 
acquired " (Eunomos, cited Chitty's Blackstone, introd. note). 



26 LOGIC 

relation of species and genus between the class 
of beings denoted by the term man and the 
class denoted by the term rational, or between 
the classes denoted by the terms horse and 
animal^ or the relation of mutual exclusion 
existing between the terms of the proposition, 
** No two islands can be contiguous/' 

§ 19. Judgment Defined. — The perception 
of a relation of signification between two terms 
is called Judgment; which may be defined as 
the intuitive perception of a significative rela- 
tion between two terms. The result of the 
process is called a judgment; which may be 
defined simply, as a self-evident proposition. 

§ 20. The Quasi-Intuitive Relations 
OF Terms. — Analogous to the intuitive rela- 
tions of terms are the relations between the 
terms of all assumed propositions, or assump- 
tions; for these, though not intuitively true, 
are assumed or supposed to be such for the 
sake of the argument, and used as principles 
from which to reason ; they may, therefore, be 
regarded as quasi-intuitive ^ Under this head 

^ We borrow this form of expression from the lawyers, who 
find it indispensable, as, e, ^., in the expressions quasi-torts, 
quasi-contracts,^'* etc. As we are informed by Cicero, the 
Epicureans held that the gods had not bodies, but quasi- 
bodies only, i. e., something like bodies. An Indian com- 
munity, I have read somewhere, were much annoyed by a 
species of animal something like cows {nielghais^ I believe 
they called them) that destroyed their crops, and the question 



RUDIMENTARY NOTIONS 2J 

are included all the relations between the terms 
of propositions assumed as premises, whether 
upon authority, or from testimony, or other- 
wise, /. e,y between the terms of all proposi- 
tions other than those that are intuitively 
perceived to be true, or that are inferred from 
other propositions. 

§ 21. The Inferred Relations of 
Terms. — The inferred relations of terms in- 
clude all relations that cannot be intuitively 
perceived from an immediate comparison of 
the terms, or that are not assumed, but that 
can be inferred by comparing the given terms 
respectively with a third or middle term, the re- 
lations of which to the given terms are known. 
Thus, e, g., we may not be able to perceive 
from a mere comparison of the two terms, that 
** Logic is a branch of the Science of Lan- 
guage,'' but by comparing the two terms of 
the proposition respectively with the middle 

arose whether it was lawful to kill them. The pundits to 
whom the question was referred were of the opinion that, 
though not cows, the animals were quasi-cows, and therefore 
not to be killed. The term will be found to be of equal 
utility in Logic as in the Law. In fact, a very useful book 
might be written on the subject — that might be appropriately 
termed Quasics. For, outside of concrete notions, all notions 
denoted by terms are formed by analogy from sensible images, 
and are quasi-things only, as, e. g., imagi7iation , refiection^ 
perception, etc. We suggest the term Quasics not with a view 
of seriously recommending it for common use, but simply for 
the purpose of directing attention to a very important subject. 



28 LOGIC 

term, ** The Science of the Term, the Proposi- 
tion, and the Syllogism, * ' the relation of species 
and genus between the subject and the predi- 
cate will be at once perceived. For** Logic is 
the Science of the Term, the Proposition, and 
the Syllogism,'* and ** The Science of the 
Term, etc.,** is a species or kind of ** the 
Science of Language,** and hence ** Logic is 
a species or kind (/. ^., a branch) of the Science 
of Language.** And so we may not be able to 
perceive from a mere comparison of the terms 
that ** the Thracians were barbarians,** but by 
comparing these terms with the middle term, 
'' Not-Greeks,'' the conclusion is apparent ; for, 
ex vi termini^ diW' Nat-Greeks'' were barba- 
rians. So, generally, using the letters X, Y, Z, 
etc., to represent the terms of any proposition, 
we may not be able to perceive intuitively the 
truth of the proposition that Z is X, yet, if it 
be intuitively perceived or assumed that Z is 
Y, and that Y is X, we may infer that Z is X. 
§ 22. Propositions and Syllogisms. — An 
immediate relation of terms, whether intuitive 
or assumed, can be expressed only in the form 
of a proposition — which may be defined simply 
as the expression of such a relation ; and an 
inferred relation, only in the form of three 
propositions constituting what is called a syllo- 
gism. The proposition may be expressed in 
the formula: Y is X; and all syllogisms in the 



R U DIM EN TARY NO TIONS . 29 

formula: Z is Y, Y is X, . • . Z is X ; or, Z is 

Y, Y is not X . • . Z is not X— the letters 
standing for terms or names, and the three 
points (. • .) being the sign of illation, and 
equivalent to the expression, '' ergo,'' or 
'' therefore."^ 

§ 23. Of Apodictic and Dialectic. — Ra- 
tiocination may consist wholly of judgments 
and inferences, or partly of these and partly of 
assumed propositions. In the former case it is 
wholly illative, or demonstrative ; in the latter, 

' To define a term (as indicated in the etymology of defini- 
tion) is in effect to establish the boundaries by which the class 
of significates denoted by it is separated from all other things ; 
and these boundaries may be conveniently represented by 
circles or other enclosed figures. These are known as Euler's 
symbols, and are extremely convenient and universally used 
by logicians. A universal affirmative proposition is expressed 
by a circle contained in a circle, the former representing the 
subject, the latter the predicate ; the universal negative by 
two circles excluding each other ; and the syllogism, by thus 
expressing its several propositions; as, e.g., in the following 
diagrams : 

Affirm. Prop. Neg. Prop. 




©0 



Affirm. Syll. Neg. Syll. 




00 



30 LOGIC 

only partially so, i, e,, only so far as the valid- 
ity of the inference is concerned. The prin- 
ciples governing the former kind of ratiocination 
constitute what is called Apodictic ; those gov- 
erning the latter, Dialectic. It will be seen as 
we progress that Apodictic is far more extensive 
in its scope or use than is commonly supposed, 
and that it includes, in fact, not only the 
Mathematical Sciences, both pure and applied, 
but also a large part of Morality, Politics, and 
Jurisprudence generally. And especially, it is 
important to observe, it includes the subject 
of our present investigations. For Logic, 
though not so treated by modern logicians, is 
strictly a demonstrative science, and will be so 
treated in this essay. ^ 

§ 24. Valid Ratiocination Illative in 
Nature. — All ratiocination, or reasoning ex- 
plicitly stated, discloses at once its validity or 
invalidity — that is to say, appears on its face 
to be either conclusive in its effect, or fal- 
lacious. Hence, all ratiocination, unless fal- 
lacious, is illative or conclusive, or, we may 
say, demonstrative in its nature. On the other 

^ One of the most universal infirmities of the average mind 
is an incapacity to distinguish (outside the mathematics) be- 
tvi^een mere opinion and apodictic^ or demonstrated truth. 
With regard to the latter, the man who is conscientious and 
accurate in his Logic may realize the fine saying of Seneca : 
" It is truly great to have in one the frailty of a man and the 
security of a god " (cited Bacon, Essays, " Of Adversity "). 



RUDIMENTARY NOTIONS 3 I 

hand, unless explicitly stated, no reasoning, 
however apparently convincing, can be re- 
garded as of this nature. Hence, from a logi- 
cal point of view, reasoning in general may be 
regarded as either valid {j. e,, illative), or as 
invalid; the latter of which may be either fal- 
lacious or simply inconsequent. The former 
may be appropriately called Logical Reason- 
ing, the latter Non-logical or Rhetorical; by 
which is meant not necessarily illogical or fal- 
lacious, but either fallacious or simply inconse- 
quent, i, e.y non-illative. 

§ 25. Right Reasoning Defined. — It is 
with the former only that Logic is directly con- 
cerned, and to it we may without impropriety 
give the name of Right Reasoning, For the 
logical quality of the reasoning does not de- 
pend upon the truth or falsity of the conclusion^ 
but upon the rectitude of the definitions^ jiidg- 
inents, and inferences. 

% 26. Logic the Art of Right Reason- 
ing. — Logic, therefore, regarded as an art, 
may be simply defined as the Art of Right 
Reasoning; and it must therefore be regarded 
as denoting the ultimate test or criterion of 
truth or error. For until the reasoning is 
made explicit, it cannot be determined whether 
it is right or otherwise. It also includes the 
doctrine of Fallacy, or Wrong Reasoning; 
but as the latter has for its end simply the 



32 LOGIC 

avoidance of error, as a means of assuring the 
rectitude of our reasoning, it may be regarded 
simply as one of the practical aspects of the 
doctrine of Right Reasoning. 

§ 27. Logic to be Regarded as Intel- 
lectual Morality. — Logic must, therefore, 
be regarded as bearing to reasoning the same 
relation as MoraHty to conduct. It may, 
therefore, be appropriately called Intellectual 
Morality, ^ 

^ Hence it is that Logic, like Morality, is not popular with 
those who disregard its precepts ; among whom are to be in- 
cluded the large majority of writers, and especially of phil- 
osophers. The principle is as expressed in the adage ; 

•' What thief e'er felt the halter draw 
With good opinion of the Law ? '* 




CHAPTER II 



DOCTRINE OF THE TERM 



OF THE NATURE OF THE TERM 



§ 28. '' Term/^ '' Name/' and '' Word '* 
Distinguished and Defined.— These words 
are often used as synonymous, but the distinc- 
tion between them is material and important. 
A zi^ord is a vocal sign, or vocable, express- 
ing a thought, or a thought expressed by such 
a sign. Under the name '* word '' is included 
the substantive or noun, and also other parts of 
speech, as, e, g,, the article, the conjunction, 
etc. A name (noun or substantive, which may 
be either simple or complex) is a word or set of 
words used to signify an object of thought re- 
garded as a thing, /. ^., as an existing substance 
or entity. The knowledge or cognition of a 
thing by the mind is called a notion or concept ; 
hence a name may be otherwise defined as a 
word, or set of words, expressing a notion, or 

33 



34 LOGIC 

as a notion thus expressed. A notion or con- 
cept is itself a thought, but it differs from 
other thoughts as being the thought of a thingy 
i, e,, of something as existing. A term is a 
name used as a subject or predicate of a pro- 
position. It is therefore to be regarded merely 
as an element of th.Q proposition ; and the pro- 
position as the principal subject in Logic. 

§29. ** Thing '' Defined. — The term 
thing is used in two different senses that 
must be carefully distinguished. In its proper 
sense the term denotes an actual thing or sub- 
stance, whether material or spiritual, as, e, g,, 
mineral, vegetable, animal, gas, man, soul, 
God, etc. In this sense things constitute the 
actual universe, and all notions or concepts 
whatever, unless false or unreal, are ultimately 
derived from them. But, in another sense, 
the term is used to denote, not only actual 
existences, or, as we may call them, real things ^ 
but mere objects of thought, or things existing 
only in contemplation of mind, and to which 
there are, in fact, no real things directly cor- 
responding.^ These may be appropriately 

' All true or real notions must correspond to real or actual 
things, but the correspondence may be either direct between 
the notion and the real things signified by the term — as in 
the case of concrete terms, e. g.^ "man," "horse," etc. ; 
ox indirect— 2,<> in the case of abstract terms — between the 
notion and the things whose attributes are signified. Thus,., 
taking for example the term " redness^'' there is apparently a 



THE TERM 35 

called quasu\^\\'c\^9>\ and of this kind are the 
concepts or notions denoted by all abstract 
terms; which denote, not real things or in- 
dividuals, but mere abstractions, as, e, g,y 
such terms as ** justice,'' ** the state,*' the 
names of the several colors, disease, death, 
etc. ; where the things denoted are not actually 
existing things, but mere concepts of qualities 
or attributes of things objectified by the 
mind. 

§ 30. ** Concept," '* Notion," and 
** Thought" Defined. — The term ''con- 
cept^'" or ''notion,'' or ''thought'' (in this 
connection we may use either indifferently) is 
a relative term implying or connoting, in its 
strict or proper sense, an individual thinking 
mind of which it is the product; and hence 
the term will have a different meaning accord- 
ing to the correlative to which it refers. It 
must therefore have many different senses; of 
which two must be especially distinguished. 
In its proper sense it denotes simply a certain 
affection of the mind of the individual; and 
in this sense, obviously, it is momentary and 
evanescent, — like the snow falling on the river, 
described by the poet, as *' ae moment white, 

direct correspondence between the notion expressed and the 
quasi'\}(\\w^ signified, though in reality they are the same ; but 
there is an indirect real correspondence between the notion of 
redness and the red things of which it is a quality. 



36 LOGIC 

• 

then gone forever." For though, it is said, 
the thought recurs to us, it is not, nor can it 
be, the same thought, but is merely a copy or 
image of it. So, when a thought — as it is said 
— recurs to us, it is always, or at least almost 
always, suggested to us by the word in which 
it is embodied ; and, as to us, so also to others. 
But Logic does not have to deal with the mo- 
mentary, fleeting thought of the individual, 
but with the thought only that is continuously, 
or we may say permanently reproduced, and 
communicated by one to another; that has be- 
come incarnate in words, and is thus, even 
when lost from the mind, at once preserved, 
and continuously suggested, or brought back 
to the consciousness of each and all. Hence, 
in Logic, the terms, notion, concept, and 
thought, are to be regarded as used in a 
secondary or derived sense, as denoting the 
common notions, concepts, and thoughts of 
mankind embodied in words. Hence the things 
or significates denoted by abstract and other 
universal terms have in fact a kind of exist- 
ence outside of any and all individual minds; 
which, as opposed to substantial, may be called 
/^^/(;<^/ existence ; /. e,, they exist in the word 
(logos), and their existence is as real and of 
precisely the same nature as that of the word 
of which they are an essential part. Hence, 
though we speak of abstractions as fictitious 



THE TERM 37 

{i, e.y feigned) or imaginary things, yet they 
are real, and in some cases, as, e, g,y in the 
case of death, disease, misery, poverty, etc., 
terribly real facts. What is meant by the term 
''fictitious tiling " is, not that the notion signi- 
fied is false or unreal, but that, for logical pur- 
poses, it is fictitiously regarded as a thing. 

§ 31. The Normal Logical Term.— 
Every term legitimate for logical purposes, 
or we may say every logical term, is therefore 
to be regarded as involving or implying three 
essential notions or elements, namely: (i) the 
vocal sign, or vocable^ (2) the notion denoted, 
and (3) the actual things, or objective realities, 
to which the notion and the vocal sign are sup- 
posed to correspond. These are all to be re- 
garded as, in one sense, essential elements of 
the logical term. For though, where the last 
is lacking, a term may exist, and it is, there- 
fore, possible to have an absurd or nonsensical 
term, yet such a term is not such as is contem- 
plated when we regard the end of Logic ; which 
is not to deal with absurdities or ingenious 
puzzles, but to discover truth and avoid error. 
Hence, an absurd or nonsensical term, or, in 
other words, a term whose signification does 
not correspond to reality, is not the normal or 
true term, essential to legitimate ratiocination; 
nor is Logic — unless in illustrating some of its 
formal operations — in any way concerned with 



38 LOGIC 

it, except to detect and expose its inherent 
vice and its essential insufficiency for logical 
purposes. 

§ 32. The Denotation and Connota- 
tion OF Terms. — All terms are regarded in 
Logic as denoting or signifying classes of in- 
dividuals/ The individuals constituting the 
class denoted by the term are marked or dis- 
tinguished by certain common attributes, at 
once common and peculiar to the class, as, 
e, g,y the class ** man '' by the mark ''rational^' 
by which it is distinguished from other kinds 
of animals. Accordingly a term is said to 
denote the individuals designated by it, and to 
connote the qualities or marks by which the 
class is determined. Thus, e, g,, the term 
** man *' denotes the class of animals known by 
that name, and connotes the quality or attribute 
of rationality by which the class is distin- 
guished. 

§ 33. The Meaning and Signification 
OF Terms. — The individuals constituting the 
class denoted by a term are said to be signified 
by the term, and are called its significates. 
Thus the term, man, denotes the class, man, 
as a whole, but signifies each and all of the in- 
dividual men composing it. The significates 
of a term may be real, — which is the case when 
they are real individuals or things, existing in 

^ See infra, § 35. 



THE TERM 39 

nature; or they may be unreal^ ox fictitious, 
i, e,, existing only in contemplation of mind; 
which is the case with all abstract terms, and 
with concrete terms where the classes of indi- 
viduals denoted are fictitiously regarded as in- 
dividuals, — as, e.g., when we speak of ** man " 
as one of the significates of ''animal.'' When 
a term denotes a class of real individuals — as, 
e.g./' man,'' regarded as denoting men gener- 
ally — its significates are real ; when it denotes a 
class of lower classes — as, e. g. , the several races, 
Asiatics, Europeans, etc. — they are unreal or 
fictitious. In the former case the term is said 
to denote an infima species ; which is to be de- 
fined as a class made up of real individuals. 
By the meaning of a term is meant both its 
denotation, or signification, and its connotation 
taken together; and the word ''meaning'* 
may also be regarded as equivalent to notion 
or concept. 

§ 34. The Extension and Intension of 
Terms. — The extension of a term corresponds 
to its denotation, or signification, and is deter- 
mined by the extent of the class denoted, or 
by the number of significates signified by it. 
The intension of a term is but another name 
for its connotation, — both words denoting 
merely the qualities or attributes, or, in other 
words, the marks by which the class is deter- 
mined. 



40 LOGIC 

II 

OF THE SEVERAL KINDS OF TERMS 

§ 35. Singular, and Common, or Uni- 
versal, Terms. — Grammatically speaking, 
terms are said to be either singular or common^ 
or, as otherwise expressed, singular or uni- 
versal. A singular term is one that denotes 
an individual or single thing, as, e.g., any par- 
ticular thing, animal, or man. A common or 
universal term is one that denotes either a class 
of individuals or a class made up of other 
classes. But in the latter case, the subordinate 
classes may be regarded as individuals consti- 
tuting the superior class; and conversely the 
individual may always be regarded as a class, — 
i. e.y 3L class of one.^ In this work, therefore, 
the distinction between singular and common 
or universal terms will be regarded as logically 
immaterial ; all terms will be regarded as uni- 
versalSy or, in other words, as denoting classes 
of significates. 

§ 36. Adjectives. — Hence also adjectives 
used as terms will be regarded as nouns or sub- 

' **By a class is usually meant a collection of individuals 
. . . ; but in this work the meaning of the term will be ex- 
tended so as to include the case where but a single individual 
exists, as well as cases denoted by the terms ^nothing'' and 
' universe ' ; which as * classes ' should be understood to com- 
prise respectively 'no beings' and 'all beings.'" — Boole, 
Laws of Thought^ p. 28. 



THE TERM 4 1 

stantives; that is to say, where a term is in 
adjective form (which can occur only with the 
predicate) it is either regarded as a substantive, 
or converted into one by adding the substan- 
tive understood. Thus, e, g,^ the proposition, 
** Man is mortal,'' is to be read: '' Man is a 
mortal," or ** a mortal being." ' 

§ 37. Abstract and Concrete Names.— 
A concrete name is one that denotes a class of 
real individuals. An abstract name is one that 
denotes qualities or attributes conceived as ex- 
isting apart from the things in which they in- 
here, or, in other words, fictitiously regarded as 
things, — as, e, g,y whiteness y strength, goodness, 
humanity, etc."^ Abstract names are commonly 
singular in form, but in their essential nature 
they are always universal. Thus, when we 
speak of virtue, the name is to be regarded as 

^ " If we attach to the adjective the universally understood 
subject, ' being ' or * thing,' it becomes virtually a substantive, 
and may for all the essential purposes of reasoning be replaced 
by the substantive. Whether or not in every particular of the 
mental regard it is the same thing to say, ' water is a fluid 
thing,' as to say, ' water is fluid,' it is at least equivalent in the 
expression of the processes of reasoning." — Boole, Laws of 
Thought^ p. 27. 

^ The distinction between concrete and abstract names cor- 
responds precisely to the distinction made by old logicians 
between names of first intention and names of second inten- 
tion. The former are names that denote real significates ; 
the latter, names that denote fictitious significates, or quasi- 
things. See further on this point Appendix I. 



42 LOGIC 

denoting, not a quality existing in any par- 
ticular man, or in itself, but the class of quali- 
ties by which all virtuous men are distinguished. 
So, though we may consider the color red^ or 
redness^ in the abstract, — dismissing from the 
mind the individuals in which it is manifested, 
— yet, upon analyzing the concept, we cannot 
fail to perceive that there are as many individ- 
ual instances of red, or, we may say, as many 
individual reds or rednesses, as there are indi- 
vidual things in which the color is manifested; 
and that red, or redness, is simply the denomi- 
nation of the class of colors thus manifested. 
Hence, abstract names, though grammatically 
singular, are to be regarded as plural, and as 
differing from concrete names only in this, that 
the individuals constituting the class are quali- 
ties, — /. ^., quasi-\.\i\v\^^, ox fictitious, not actual 
existences, — and that among the marks by 
which the class is distinguished are the actual 
individuals in whom alone the qualities exist. 
An abstract name is therefore to be regarded 
as denoting a class of qualities ; and as connoting 
the individuals in which they inhere. 

§ 38. The Distinction of Fundamental 
Importance. — The distinction between con- 
crete and abstract names, or names oi first, and 
of second intention, is one of fundamental im- 
portance. In dealing with the former, the 
things denoted by the names we use are ever 



THE TERM 43 

present to the mind, and we may therefore, as 
is asserted by Mill, be said — without violent 
absurdity — to deal with things^ rather than 
with notions or names. But where we deal 
with abstract terms, the things present to the 
mind are mere abstractions, fictitiously re- 
garded as things; and we are, in fact, dealing 
not with things, but with ^^/^^/-things only.' 

§ 39. Positive and Negative Terms. — 
The distinction between positive and negative 
terms is also one of fundamental importance 
in Logic. By this division of terms the whole 
universe of things, real and fictitious^ is divided 
into two classes, the one marked by having, 
the other by not having, a certain quality or 
qualities, as e, g,, white things, and things 
that are not zvhite ; and it is obvious that to 
each positive there must be a corresponding 
negative term, 

§ 40. Of the Universe of the Proposi- 
tion. — But ordinarily in speech we have in 
view a more limited class, and must be under- 
stood to refer, not to the universe of things, 
but to some class less than the universe, but 
superior to the classes denoted by the subject 
and predicate; and this superior class is said 
to constitute the universe of the proposition in 
which the terms are used. Thus, when we 
speak of ** mortal" and ** immortal," the class 

^ See Appendix K. 



44 LOGIC 

of ** living things'' or ** beings'' is obviously 
referred to as the superior class, and is, there- 
fore, said to constitute the universe of the 
proposition; and the division is to be under- 
stood to be into ** mortal" and *' immortal" 
beings. So, in the proposition, ** Brutes are 
irrational," the superior class we have in view 
is that of animals, and this class is to be re- 
garded as the universe of the proposition; as 
(denoting ''not'' by the Greek privative, a) 
may be illustrated by the following diagrams, 
either of which may be used : 








OF THE ANALYSIS OF TERMS 

§41. Apprehension. — As it is the func- 
tion of Logic to compare the notions de- 
noted by terms, with the view of determining 
their relations, a preliminary process is essen- 
tial ° namely, that of apprehending or under- 
standing the significations of terms; which is 
called by logicians, *' Simple Apprehension." * 

* The operations of the mind involved in reasoning are (i) 
Simple Apprehension, (2) Judgment, and (3) Inference (see 



THE TERM 45 

This is effected by means of what may be 
called the *' Analytical Processes "; which will 
next be considered. 

§42. Analytical Processes. —As pre- 
liminary to apprehension, it is essential that 
the sense in which the term is to be used shall 
be identified, or, in other words, that of the 
several senses usually denoted by a vocable, 
one shall be selected. This is often called 
nominal definition {i, e,, definition of the name), 
but improperly; for until it is determined in 
what sense a term is used, there is in fact no 
name. Hence we call it. Vocal Definition^ i. e.. 
Definition of the Vocable, Next, it is necessary, 
before the two terms can be compared, to ap- 
prehend, in the case of each of them, the sig- 
nificates of the term, or the class of significates 
denoted by it ; for otherwise we will not be 
able to compare their significations. This is 
effected by the definition of the term; which, 
to distinguish it from vocal, is called nominal 
or real definition ^ ; and this again involves the 
process of classification or division, 

Whately, Logic), I have altered the ordinary statement of 
these operations by substituting for the third "Inference" 
instead of "Discourse"; which is commonly defined as 
"reasoning" or "ratiocination." But, as used in this work, 
these words include both Apprehension and Judgment. 

^ There is some confusion among logicians as to the use of 
the terms. Nominal Definition and Real Definition. By some, 
the former term is used as denoting what I have called vocal 



46 LOGIC 

§ 43. Vocal Definition.— A word, or vo- 
cable,—/, e.y the vocal sign, — has usually many 
significations; and commonly, in using it, we 
do not, at first, distinguish between such of the 
notions denoted by it as are nearly the same, 
but, instead of regarding it (as we should) as 
part of several names, use it as though it were 
a single name. But in thus using a vocable 
without distinguishing its several senses, it is 
inevitable that, in the course of the ratiocina- 
tion, it will be used in a shifting sense, or 
rather, we should say, in several senses, as 
suggested by the varying occasion ; and that 
the coherency of our reasoning will thus be 
destroyed. This fault in ratiocination is called 
the fallacy of cortfusion or of ambiguity, and, 
as will be seen in the sequel, is one of the most 
common and most serious of fallacies. Hence 
it is one of the most important and imperative 
of logical rules that, in the case of every word 
we have occasion to use in our reasoning, the 
sense in which it is to be used shall be clearly 

definition ; but this seems to be incorrect. According to the 
better usage, a Nominal Definition is a definition of the 
Notion expressed in a term ; and hence Whately says " that 
Logic is concerned with nominal definitions only." To this 
Mansel objects on the ground that '* Logic is concerned with 
real or notional definitions only ; its object being to produce 
distinctness in concepts^ which are the things of Logic " (Han- 
sel's Aldrich, p. 39). But this is precisely what Whately 
means ; and says. 



THE TERM 47 

distinguished and consistently observed. And 
this indeed, ex vi termini^ is essential even to 
the beginning of ratiocination; for, until this 
is effected, we have not even that essential 
material of ratiocination, a namej with which 
to deal. The vocal definition of a term may 
be effected in various ways, — as, e, g,, by the 
use of any other term, or phrase, or sentence 
of equivalent signification ; or, negatively, by 
rejecting those senses of the word that we do 
not wish to use; or, often, by an imperfect 
definition, as by simply specifying the genus of 
the class denoted by the term ; or, in fine, by 
any means that may serve to confine the term 
to one sense only, and thus to prevent am- 
biguity. 

§ 44. Division and Classification. — 
Division consists in distributing the class of 
significates denoted by a name into subordinate 
classes, with appropriate names; classification 
in the reverse process of assigning a class de- 
noted by a name to a class denoted by another 
name. 

§ 45. Genus and Species. — In the former 
case, the class distributed is called the genus ; 
the classes into which it is distributed, species. 
In the latter, the class assigned is a species, the 
class to which it is assigned, the genus. The 
genus and species, however, as in the case of 
synonyms, may be of equal extension. 



48 LOGIC 

§ 46. Division. — Division is an act of Anal- 
ysis ; Classification, of Synthesis, But the 
same principles govern both, and the elucida- 
tion of one will equally explain the other. In 
Logic, the analysis of terms is the more im- 
portant process, and we will therefore adopt, 
as the subject of explanation, the process of 
Division. The term to be divided, or, rather, 
the class denoted by the term, is, as we have 
said, called the genus; the subordinate classes 
into which the genus is divided, species. The 
species must, of course, be exclusive of each 
other, — i, e.y they must not overlap; and taken 
together they must exhaust the genus. Thus, 
the term thing — meaning thereby things and 
quasi'things — may be divided, and subordinate 
classes subdivided, as follows : 

Things 



Real Things Quasi-Things 



Bodies Not Bodies 



Organic Inorganic 



r \ 

Animal Not Animal 

A . 



Rational Not Rational 
etc. 



§47. Dichotomy. — It will be observed 
that the above division is, in each case, two- 



THE TERM 49 

fold, — i. e,, into two classes, represented by 
a term and its negative. This is called Dichot- 
omy, and, as in using it we are less liable to 
error than in other modes of division, it is 
most commonly used. The genus may, how- 
ever, be divided into three or more species, pro- 
vided the species taken together exhaust the 
genus, and be exclusive of each other, — as, e, 
g,, in the division of Bodies into (i) Inorganic, 
(2) Vegetable, and (3) Animal. 

§ 48. Nominal Definition of Terms. — 
The definition {i. ^., the real or nominal d^^m- 
tion) of a term consists in assigning the class 
denoted by it to an appropriate genus, and 
giving its specific difference ; by which is meant 
some mark or marks peculiar to it, by which it 
may be distinguished from other species. It 
is, therefore, a species of classification, — /. ^., 
it consists simply in classifying the given class, 
or species, by assigning it to a genus, and in 
adding also the appropriate marks, or specific 
difference, by which it is distinguished from the 
other species contained in the genus. The 
definition of a term is, therefore, to be regarded 
simply as a complete classification of it; and 
the classification of it as an incomplete or im- 
perfect definition. But the latter has the ad- 
vantage that it can often be used where the 
former would be inconvenient or impossible. 

§49. The Essence of the Term. — A 



50 LOGIC 

quality at once common and peculiar to the in- 
dividuals denoted by a term is called 2, property 
of the class denoted ; a quality common to the 
class, but not peculiar to it, is called an acci- 
dent.^ The definition of a term is made up by 
selecting from the accidents of the term one to 
serve as a mark for the purpose of determining 
the genus, and from the properties one to serve 
as specific difference. These together constitute 
the essence of the term ; which will therefore 
vary with the definition, and be determined by 
it. Thus, e, g,, if we define man as a rational 
animal, ''animaV will be the genus; ''ra- 
tional'' the specific difference; ''talking,'' 
' ' laughing, " " cooking, ' ' etc. , properties ; ' ' mor- 
tal," " carnivorous,'' " mammal," etc., acci- 
dents. But we may, if we choose, define him 
variously as a talking, laughing, or cooking, 
mortal, carnivore, or ma7mnaL The essence of 
a term is therefore but another name for the 
meaning of the term. Properties not used for 
specific difference, and accidents not used for 
genus, do not enter into the essence of the term. 

^ There is much confusion among logicians in the use of the 
term accident. The definition in the text is that of the best 
authorities, including Aristotle ; and the term should be con- 
sistently thus used. 




CHAPTER III 

DOCTRINE OF THE PROPOSITION 

I 

RUDIMENTS OF THE DOCTRINE 

§ 50. Proposition Defined. — A proposi- 
tion may be defined as the expression of a rela- 
tion of signification between two ternis; which, 
of course, implies the expression of the corre- 
sponding relation between the notions ex- 
pressed in the terms. 

§ 51. The Grammatical Proposition. — 
But here there is a difference between Logic 
and Grammar, or, we may say, between the 
logical and the grammatical proposition. In 
the latter, any of the innumerable relations ex- 
isting between terms, or, what is the same 
thing, between the things denoted by them, 
whether past, present, or future, may be ex- 
pressed as existing between the terms; and the 
relation may be expressed by any copula or 
connecting word, or the same word may be 

51 



52 LOGIC 

used to express both copula and predicate, as, 
^' S"> '' John struck William '' ; *' The sun will 
rise at six o'clock to-morrow**; '* It rains'*; 
** The Carthaginians did not conquer Rome/* 
etc. But in Logic the only copula used is the 
present tense of the verb ''to be,'' with or 
without the negative particle ; and the only in- 
terterminal relation considered is that of species 
and genus; which may be either affirmed or 
denied. 

§ 52. The Logical Proposition. — Ac- 
cordingly the logical proposition is of two 
forms, the affirmative and the negative. In 
the foVmer the relation of species and genus 
between the terms is affirmed, — as, e, g,y ** Man 
is mortal,** ** Y is X,** etc. ; in the latter it is 
denied, — as, e, g., *' Man is not perfect,** '' Y 
is not X,** etc. The affirmative proposition 
may be read, either, ** Y is X,** or ** Every Y 
is X,** or ** All Y*s are X*s ** ; or, to take the 
concrete example, '* Man is mortal,** or 
'' Every man is mortal,** or ** All men are 
mortal,** — these expressions being all equiva- 
lent, and signifying equally that the subject 
class — ^or class denoted by the subject — is a 
species of the predicate class. The negative 
proposition may be read either as above or as 
follows: '' No man is perfect,** " No Y is X,** 
etc. It is a cardinal postulate in Logic that all 
propositions may, and indeed — for purposes 



THE PROPOSITION 53 

of logical analysis — must be converted into 
logical form; as, e, g., the above examples 
into the following : ** John is the man who 
struck William " ; ** Six o'clock is the hour at 
which the sun will rise to-morrow''; '' Rain 
is falling"; '' The Carthaginians are not [or, 
grammatically, we should say, '' were not "] 
the conquerors of Rome." * 

§ 53. Interpretation of the Logical 
Proposition. — In all logical propositions the 
copula is to be interpreted as meaning '* is con- 
tained m'' or*' is a species ofy'' or the contrary, 
as the case may be."^ Hence in Logic the only 

^ There are commonly recognized by logicians four forms of 
the proposition, designated respectively by the letters, A, E, 
I, and O, and called the '' Universal Affirmative,''' the ^'Uni- 
versal Negative^^'' the ''^Particular Affirmative,'' and the 
'''Particular Negative" (see infra, §88). But if in I 
and O we regard the expression "some Y" — instead of 
" Y " — as the subject of the proposition, these forms will be- 
come the same as A and E. Hence, propositions may, as in 
the text, be regarded as of two kinds only, namely, affirma- 
tive and negative ; the former affirming that the subject is 
included in the predicate class ; the latter denying that it is so 
included. This distinction agrees precisely with our defini- 
tion, and will be sufficient for our present purposes, and, 
indeed, for all practical purposes. 

^ The affirmative proposition " Y is X " is to be construed as 
asserting that the class Y is wholly included in the class X ; the 
negative, " Y is not X," that it is wholly excluded. But the 
class Y may denote a part of a class, as, e. g., " Some A" ; 
in which case the proposition *' Y is X," or " Y is not X," 
would be equivalent to the ordinary forms, "Some A is X," 
or " Some A is not X," 



54 LOGIC 

significative relation recognized is the relation 
of the inclusion or exclusion of the subject 
class in or from the predicate : and accordingly 
this may be called appropriately the logical 
relation. Yet the logical proposition is not less 
capacious of expression than the grammatical; 
for, as the latter may always be converted into 
the former, it follows that all relations may be 
expressed in the one as in the other. The 
only difference is that in the grammatical prop- 
osition the relations between the notions in- 
volved may be expressed either in the copula, 
or in the terms themselves; while in the logical 
proposition the only interterminal relation ex- 
pressed (/. ^., affirmed or denied) by the copula 
is that of species and genus, and all other re- 
lations between notions are expressed in the 
terms, — /. ^., in complex terms.' 

§ 54. The Conversion of Propositions. 
— By conversion is meant the transposition of 
subject and predicate — i, e,, making the predi- 
cate the subject, and the subject, predicate. 
But, such conversion, to be legitimate, must be 
illative, i, e,, the force or conclusiveness of the 
proposition must not be affected. Thus the 
proposition, *' Y is not X " (since the subject and 
predicate classes are mutually exclusive), may 
be converted into the proposition, ** X is not 

^ This is admirably illustrated by Mr. Boole's system of 
signs, of which I append an epitome. See Appendix L. 



THE PROPOSITION 55 

Y/* which is called simple conversion; and so 
with all definitions, and other equational prop- 
ositions; and also with the particular affirma- 
tive proposition, ** Some Y is X/' But the 
affirmative proposition, ** Y is X,'* cannot be 
thus simply converted; for the subject class is 
identical with only ** some" of the predicate 
class, and in conversion the predicate must be 
qualified by that particle, thus substituting a 
new term. Or, symbolically, the proposition, 
** Y is X,*' can be converted only into the 
proposition, '' Some X is Y *'; which is called 
conversion per accidens. 

II 

SEVERAL THEORIES OF PREDICATION 

§ 55. The Copula. — In the logical proposi- 
tion, as we have seen, the copula is interpreted 
as meaning *'is contained in,'' or the contrary ^ 
and this is the traditional, or, as it may be 
called, orthodox, theory of predication. But 
the copula may be otherwise interpreted ; and 
from these several interpretations several theo- 
ries of predication will result. Of these, two 
may be distinguished as requiring some remark, 
namely, the Equational Theory, in which the 
copula is interpreted as meaning, ** is equiva- 
lent to,'* and is expressed by the sign of equiv- 
alence (=) ; and the Intensive Theory, where it 



$6 LOGIC 

IS interpreted as meaning, ** has the quality or 
attribute,'" Thus, e, g,, the proposition, '* Man 
is rational,'* is interpreted according to the 
Traditional Theory as meaning, ** the class 
man is contained in the class rational'* ; ac- 
cording to the Equational Theory^ as meaning, 
** the class man is the same as the class 
rational'' ; and according to the Intensive y as 
meaning, ** the individuals constituting the 
class man have the quality or attribute^ rational^ 
or of rationality/' 

§ 56. The Equational Theory.— In the 
logical proposition, the classes denoted by the 
subject and predicate may be equal; for, where 
this is the case, each may be said to be con- 
tained in the other. Hence in such cases the 
proposition is always convertible, as, e, g., we 
may say indifferently that ** man is a rational 
animaly' or that ''a rational anijual is a man,'' 
or, generally, if Y = X, either that " Y is X ** 
or ** X is Y.'' Such propositions are recog- 
nized and used in the traditional Logic, as in 
the case of definitions, and in other cases, 
but it is not thought necessary to express the 
equivalence of the terms. Hence in the affirm- 
ative proposition *' Y is X " it cannot be deter- 
mined from the form of the proposition whether 
X is of greater extension than Y, or of the 
same extension. 

§ 57. Quantification of the Predicate. 



THE PROPOSITION 57 

— The modern doctrine of "" the quantification 
of the predicate '' has for its object to remedy 
this supposed defect by expressing in every 
proposition by an appropriate sign the quan- 
tity of the predicate, or, in other words, by in- 
dicating whether it is distributed or not^ ; and 
this is effected by prefixing to the predicate a 
sign indicating the relation of quantity between 
it and the subject, and giving to the propo- 
sition an equational form. Thus, e. g,, the 
proposition, ** Y is X,'' may be expressed in 
the form ** Y = vX,'' which is the method of 
Boole; or in the form *' Y == YX," which is 
the form proposed by Jevons, and is read, 
*^ Y = the part of X that is Y," or ** the Y's 
are the X's that are also Y's/' Or, more sim- 
ply, instead of the proposition, *' Y is X," we 
may say, ** Y is a certain species of X '*; or, 
to take a concrete example, instead of the 
proposition, '' Man is an animal,'* we may say, 
** Man is a certain species or kind of animal/' 
Hence, whether an equational proposition shall 
be expressed in the traditional or in the equa- 
tional form is a matter of choice to be 
determined by convenience. Generally the 

^ A term is said to be " distributed " when it is taken uni- 
versally, i. e., where the other term of the proposition is, or 
may be, predicated of all the individuals denoted by it, as, e. g. , 
the subject of a universal affirmative, or either subject or 
predicate of a universal negative proposition (see § 87). 



58 LOGIC 

traditional form is sufficient, as we can readily 
determine from the matter of the proposition 
whether it is to be regarded as equational or 
otherwise. But in the mathematics the equa- 
tional form is much the more efficient, and is 
therefore always used. 

§ 58. The Intensive Theory.— The differ- 
ence between the traditional and the intensive 
theory of predication is that, in construing the 
proposition, we have regard in the former to 
the extension of the terms only ; but in the 
latter, in construing the predicate, we have re- 
gard to its intension. Thus, when we say ** Man 
is mortal,'* we mean, in the former case, that 
the class man is contained in the class mortal ; 
but in the latter, that man has the quality or 
attribute of mortality. But the latter expres- 
sion means nothing more than that " the qual- 
ity of mortality is contained in, or among, the 
qualities of man " ; which is itself an extensive 
proposition. Hence the intensive interpreta- 
tion of the proposition simply results in an 
extensive proposition in which the qualities 
of the original terms are substituted for its 
original significates, and the terms inverted. 
Thus, e, g,^ if we denote by Y^ the qualities of 
Y, and by X^ the qualities of X, the proposi- 
tion, Y is X, may be converted into X^ is Y^; 
which may be called Intensive Conversion^ or 
conversion by Intensive Interpretation, 



the proposition 59 

§ 59. Traditional Theory of Predica- 
tion. — Even under this theory the proposition 
seems to be susceptible of several interpreta- 
tions. Thus, e, g,y we have interpreted the 
copula as meaning ** is contained in " or ** is a 
species of '' ; and again we may interpret it as 
meaning that the significates constituting the 
subject class may each and all be called by the 
name constituting the predicate — or, in other 
words, that the name predicated belongs to 
the significates of the subject term, or of any of 
them ; which has been called interpreting the 
judgment *' in its denominatioit " (Thompson's 
Laws of Thought y § 195). But for all logical 
purposes these interpretations are practically 
the same, and it will make no difference whether 
the proposition be interpreted in the one way 
or the other. This is sufficiently obvious with 
regard to the expressions, ** is contained in,*' 
and ** is a species of " ; and is equally true of 
the interpretation suggested by Dr. Thompson. 
For, taking as an example the proposition, 

Man is an animal," it is obviously indifferent 
whether we construe it as meaning ** the class 
man is included in the class animal,'' or that 
*' it is a species of the class animal,'' or that 

the name animal is applicable to all signifi- 
cates of the name man," These varieties of 
interpretation will, therefore, not demand a 
further consideration. 



6o LOGIC 

% 60. Collective and Distributive In- 
terpretation. — There is, however, another 
difference of interpretation it is important to 
consider; and especially with reference to 
mathematical reasoning, which is to be con- 
sidered presently. Common terms, or terms 
denoting classes of more than one, may be used 
either collectively or distributively, — i, e.y the 
class denoted by the term may be regarded 
either as a whole made up of individuals,^ or as 
a number of individuals constituting a class, or 
signified by the name. Thus, e, g., the term 
** man '' may be used to denote either the class 
** man," as when we say, ** Man is mortal'*; 
or the individuals composing the class, as 
when we say, *' A man is a mortal,'' or ** Men 
are mortals." Whether a term is used collec- 
tively or distributively may be indicated, as in 
the above examples, by the expression, or may 
be simply understood ; or the expression may be 
such as not to indicate either expressly or im- 
plicitly whether the term is used in the one way 
or the other. With regard to the subject of the 
proposition it is logically imrnaterial in which 
way the term is used. Thus, in the proposi- 
tion, * * Y is X, " the subject is used collectively ; 
and in the proposition, '* All Y's are X's," or 

^ When a concrete term is construed collectively, it becomes 
abstract, and is to be regarded as denoting, not a number of 
real individuals, but one quasi individual only. 



THE PROPOSITION 6 1 

'' Every Y is an X/^ or ^^ A Y is an X," distri- 
butively ; but the forms are logically equivalent. 
So with regard to the predicate, where the 
terms are of equal extension, it is immaterial 
whether it be construed collectively or distribu- 
tively, provided, if the predicate be construed 
collectively, that the subject also be thus con- 
strued. For to construe a term collectively is 
to regard the class denoted by it as an individ- 
ual, and a term thus construed is therefore to 
be regarded as a singular term. But a singular 
term cannot be predicated of any but a singu- 
lar term, with which it must exactly conform 
in signification; or, in other words, a singular 
term can be predicated of another singular term 
only in the equational proposition. Thus, 
e, g.y in the proposition, '* Y is X," it is im- 
material whether we regard Y as denoting the 
class Y, or as signifying the significates com- 
posing the class. But the class X cannot be 
construed collectively unless we also construe 
the class Y in the same way, and unless also 
the two classes are co-extensive, or, in other 
words, unless the proposition can be put in the 
form, Y = X. 

Ill 

OF THE PREDICABLES 

§ 6i. Definition and Division of the 
Predicables. — A predicable may be defined 



62 LOGIC ' 

as a term that may be made the predicate of an 
affirmative proposition. As explained above, 
such propositions may be either eqitational or 
non-eqitational. In the former case the predi- 
cate is of the same extension as the subject; in 
the latter, of greater extension. All predi- 
cables, therefore, may be divided into two 
classes, — namely, those that are equivalent to 
the subject, and those that are not equivalent. 
An equivalent predicable may be either defini- 
tion ox property ; for each of these is precisely 
co-extensive with the subject (§ 49). Non- 
equivalent predicables must be either genera 
or accidents ; either of which may always be 
predicated of the subject (/^.)- This is the 
division of predicables used by Aristotle. 

§62. Tv^OFOLD Division of Predicables. 
— But the distinction between '' definition " and 
** property '* seems, with. relation to the subject 
of predicables, to be unimportant; for ''prop- 
erty'' differs from ''definition'' only in the 
use made of the former (/i^.). And so with 
reference to the distinction between genus and 
accident {lb.). Hence it has been proposed 
'* to abandon, as at least unnecessary for logical 
purposes " (or rather, we should say, for pur- 
poses of predication), ' ' the distinctions between 
property and definition, genus and accident, 
and to form, as Aristotle has also done, two 
classes of predicables ; one of predicables taken 



THE PROPOSITION 63 

distributively and capable of becoming subjects 
in their respective judgments without limita- 
tion ; the other of such as have a different ex- 
tension. In the former the predicable has the 
same objects [/. ^. , significates] as the subjects, 
but different marks, or a different way of rep- 
resenting the marks. In the latter there is a 
difference, both in the marks and the objects '* 
(Thompson*s Lazvs of Thought^ § 69.)^ 

§ 63. One Kind of Predicables Only. — 
But even the twofold division of predicables, 
into equivalent and 7ioii-eqiiivalent, is, from the 
traditional standpoint, of minor importance; 
for, as we have seen, the old Logic ordinarily 
takes no account of equational propositions, 
but these, like others, are regarded as import- 
ing simply the inclusion of the subject in the 
predicate; and in this mode of interpreting 
the proposition, we have, in effect, a complete 
doctrine of the predicables. 

^ The division of predicables most commonly used is that of 
Porphyry (Aristotle's Logical Treatises, Bohn's edition, Intro- 
duction of Porphyry ; also Jevons's Lessons in Logic, p. 98). 
According to this division, '' Specific Difference^' is substituted 
for the " Definition " of Aristotle's division, and there is added 
as a fifth predicable, " Species,'' as being predicable of individ- 
uals. But, as observed by Mansel (Aldrich's Logic, Preface), 
'*v^hether this classification is an improvement, or is consist- 
ent v^ith the Aristotelian doctrine, admits of considerable 
question." The view taken in the text is in every respect 
preferable (Thompson's Laws of Thought, pp. 136 et seq.). 



64 LOGIC 

IV 
OF THE RELATIONS BETWEEN TERMS 

§ 64. Of the Relations of Terms Gen- 
erally. — The end of Logic is to determine 
the relations, and, as involved in this, the defi- 
nitions, of terms, or (what is the same thing), 
of the notions expressed in terms (§ 16). Of 
these notions, the most conspicuous are those 
existing between what are called relative words 
— as, e. g,, father and son, wife and husband, 
higher and lower, etc., and also the active 
and passive forms of the verb, and all in- 
flections of verb or noun, or, in a word, all 
paronyms, etc. But the term, relative, though 
applicable, is not peculiar to this class of 
words, and is, therefore, not altogether appro- 
priate. Relations, more or le^s apparent, exist 
between all terms, and in the development 
of these consists the raison d' etre of Logic. 
Hence, properly speaking, no term can be said 
to be absolute, as opposed to relative. For — 
to consider only one of the most general of re- 
lations — any thing, or class of things (real or 
fictitious), must always be assignable to one of 
two classes, namely the class denoted by a 
given term, or to the class denoted by its 
negative ^ ; and, in addition to this universal 

^ This, of course, is true only on the assumption that we 
reject Particular Propositions, as proposed (§ 52, note). 



THE PROPOSITION 65 

relation, there are numerous others, either of a 
general character, — as e, g,, the relation be- 
tween numbers, or other expressions of quan- 
tity, — or such as are peculiar to certain words, 
— as, e, g,, between hunger and animal, hunger 
and edible, gravity and body, fish and water, 
the sun and the planets, etc. In fine, the re- 
lations between terms are innumerable, and, 
when the significations of terms are appre- 
hended, these relations may, in general, or, at 
least, in innumerable cases, be either intui- 
tively perceived, or demonstratively inferred. 

§ 65. Of the Several Kinds of Inter- 
terminal Relations. — The relations of 
terms are, for various purposes, divided in so 
many different ways that it would be impracti- 
cable to enumerate them. But, of these divi- 
sions, there are three that, either on account of 
their intrinsic importance, or of the importance 
attributed to them by logicians, will require 
our attention. These consist in the distinction 
made (i) between the Predicables and the Cate- 
gories or Predicaments ; (2) between the formal 
and the material relations of terms; and (3) be- 
tween the relations that are intuitively per- 
ceived, and those that are not, or, more briefly, 
h^tv^Q^^n Judgments and assumptions (§19, 20). 

§ 66. (i) Of the Predicables and of the 

Otherwise we would fall into the same fallacy as Jevons and 
Hobbes (v., infra, § 90 and note). 
5 



66 LOGIC 

Categories or Predicaments. — The dis- 
tinction between these corresponds precisely to 
the distinction we have made between the 
logical and the grammatical forms of the prop- 
osition. Etymologically both terms are of the 
same import, — denoting simply terms that may 
be predicated of other terms, i. e., that may be 
made/r^<^/r^/^^ of propositions; but, according 
to inveterate use, the former term relates ex- 
clusively to the logical proposition, the latter, 
to the grammatical. There is, therefore, an 
essential difference between the Doctrine of 
the predicables and that of the Categories 
or predicaments. The former — which treats 
simply of the relation of species and genus be- 
tween the terms expressed in the logical prop- 
osition — has already been considered. The 
latter treats of all the various relations that 
may exist between the terms of the grammati- 
cal proposition ; and, as these include all rela- 
tions, whatever, that may exist between terms, 
or between their significates, it follows that the 
categories or predicaments are to be understood 
as denoting the most general classes into which 
such relations may be distributed. By such a 
classification— if it could be accomplished — all 
relations between terms and between things 
-would be developed, and thus a basis furnished 
for a classification of all possible predicates. 
But the subject is one of difficulty, and in the 



THE PROPOSITION 6/ 

present state of philosophy, a satisfactory treat- 
ment of it is impracticable. It would simply 
serve, therefore, to confuse the student, if we 
should enter upon it, and we will accordingly 
omit it. 

§ 67. (2) Of the Formal and of the Ma- 
terial Relations of Terms. — By ih^forjnal 
relations of terms are meant those relations that 
are universal in their nature, — i. e.y that exist 
generally with reference to all terms; as, e, g,, 
the relation between terms and their contra- 
dictories, between a term used universally and 
the same term used particularly, between the 
subject and the predicate of the proposition, 
etc. These are all apparent at once from the 
mere expression, without taking note of the 
matter of the term, except in so far as it is 
universal or common to all terms. Thus, e. g,, 
in the expression ** not-man " we perceive at 
once a formal relation between this term and 
" man," and in this case the privative ** not," 
though part of the matter of the term not- 
man, is the ground of the relation; which is 
formal because universal. And so, in the 
terms '* Y " and '* some Y," d^ formal relation 
is apparent, though the word * * some " is in fact 
part of the matter of the term '' some Y/' 

Hence, the distinction between the formal 
and the material relations of terms does not, 
as is commonly supposed, rest upon the 



68 LOGIC 

distinction that, in the former case, the matter 
of the term is not considered, and, in the latter, 
that it is ; but on the distinction that the formal 
relations are based upon such part of the mat- 
ter or meaning of terms as is common to all or 
to many terms, and with that regard to the 
material relations this is not the case. 

Hence, logically, there is, in fact, no essential 
difference of nature between the two kinds of 
relation. For the material relations between 
terms are as apparent and as certain as the so- 
called y^^r^^/ relations, — as, e,g,^ the relations 
between relative terms, as *' father'* and " son,'' 
etc., or those between such terms as *^ island " 
and *^ continent," *' island " and ** water," 
"body" and ** weight," *'five" and "seven,'' 
" nine " and " fifteen," etc. ; and they differ only 
in this, that these subsist only in particular 
cases, and not universally. Hence the notion 
that would restrict the functions of Logic to the 
vatr^Xy formal relations of terms is based upon 
an unessential difference of nature between 
these and other relations, and therefore cannot 
be sustained. 

§ 68. (3) Of Judgments and Assumptions. 
— Of the immediate relations between terms 
some — as we have seen — are self-evident, or 
may be intuitively perceived ; others are not 
of this character. Where the relation between 
the terms of a proposition is of the former 



THE PROPOSITION 69 

kind, it IS called ^Judgment ; where the rela- 
tion expressed is of the latter kind (if not 
an inference) it is called an assumption (§§ 
19 et seq,). This division of propositions is 
based upon an essential difference of nature, 
and is one of fundamental importance. It 
will therefore require our most attentive con- 
sideration. 

Logical Judgment Defined. — In the logi- 
cal proposition, the only relation between 
the terms expressed is w^hat we have called 
the significative relation, — i. e,, the relation 
of inclusion or exclusion of one of the term^ 
in or from the other. Hence judgment, in 
the logical sense, may be defined as consist- 
ing in the intuitive perception of a significative 
relation between two terms, — i, e,, in the in- 
tuitive perception that the subject class is, or 
is not, included in the predicate class, — as, 
e, g.y where, from our knowledge of the signi- 
fication of the terms, we afifirm that ** man is 
an animal,*' or that *' fishes are denizens of the 
water,'* or that ** bodies are affected by grav- 
ity,'* or that ** fortitude is the only resource 
against the inevitable," or, in the Latin, 
* * Quidquid erit superanda omnis fortuna ferendo 
estr 

% 69. Of the Distinction between 
Judgment and Assumption.— The product 
of this mental process — as we have seen — is 



70 LOGIC 

called 2, judgment ; which may be defined as 
a proposition at once self-evident, and not in- 
ferred from another proposition or proposi- 
tions. Hence, the opinion that ** propositions 
are judgments expressed in words'' is a de- 
parture from the logical definition of a judg- 
ment. A judgment expressed in words is a 
proposition, but the converse is not true. For 
where a proposition is based not merely upon 
a comparison of its terms, or upon an inference, 
but upon extrinsic evidence, or authority, or 
other grounds, the forming of an opinion is 
not a logical process, and the proposition, from 
a logical point of view, is to be regarded, 
not as a judgment ^ but merely as an assump- 
tion or hypothesis. Of this kind is the prop- 
osition that Pompey's army was defeated at 
Pharsalia; that Cicero was murdered by the 
Triumvirate ; that a given policy as, e, g,, 
protection to home industries, or the remon- 
etization of silver, will be beneficial, etc. 

§ 70. Of the Distinction between 
Apodictic and Dialectic (§ 23). — Hence 
it may be readily perceived how inadequate 
IS the conception of Logic that would re- 
strict its functions to merely formal infer- 
ence to the exclusion of judgments; or the 
conception of demonstrative or apodictic rea- 
soning that would confine it to the mathe- 
matics ; or to the limited class of sciences that 



THE PROPOSITION J I 

rest upon intuitions, in the sense of the term 
used by modern metaphysicians ; or that would 
exclude from it all reasoning originating in 
judgments involving empirical notions or con- 
cepts. For, logically, a judgment as to a sig- 
nificative relation between two terms denoting 
notions or concepts, of which the apprehension 
is empirical, — as, e, g,y the judgment that 

bodies are affected by gravity,*' that ** fish 
live in water,** that ** food will assuage 
hunger,** etc., — is quite as self-evident as the 
judgment that '' two and three are five,** or 
that ** sixty-four is the square of eight.** In 
fact, the two classes of judgments are, logi- 
cally, of precisely the same nature, — each 
being but an intuitive perception of a relation 
between the significations of two terms; as 
follows from our definition. 

§ 71. No Distinction in Logic between 
A PRIORI AND Empirical Notions. — Logic, 
therefore, takes no account of the metaphysical 
distinction between a priori and empirical no- 
tions, but regards all judgments as intuitive. 
Its function is simply to determine the relations 
existing between the significations of terms; 
and if the significations of the terms com- 
pared be apprehended, and be of such nature 
that the relation between them can be per- 
ceived, either immediately — i, e, intuitively, 
— or by intermediary comparison with other 



72 ' LOGIC 

terms, the conclusion reached — which ex- 
presses merely the relation between the signi- 
fications of the terms — is, so far, absolutely 
true. 

§ 72. Of the Error that Ratiocination 
IS ONLY Hypothetically True.— Hence 
it is an error to suppose that ratiocination is 
only hypothetically true, or, in other words, 
that Logic is not concerned with the truth of 
premises. In many cases this is so; but it is 
true in no case in which the ratiocination pro- 
ceeds from judgments exclusively. For in all 
such cases the premises — which, as we have 
said, merely express significative relations be- 
tween their terms — are not merely assumed, 
but are intuitively known to be true, and the 
conclusion is true, not hypothetically but ab- 
solutely. 

And this is essentially the case even where 
the notions involved in the original judgments 
or premises are themselves false or unreal; for 
the ratiocination has for its direct object only 
to determine correctly the relation between 
the significations of the terms of the con- 
clusion ; and all that is directly asserted in 
the conclusion is that the signification of the 
terms are related as expressed ; and hence, 
when the ratiocinative functions have been 
rightly performed, the conclusion must be 
necessarily true. But as it is necessary for 



THE PROPOSITION 73 

purposes of ratiocination that grammatical 
propositions be converted into logical, so also, 
for practical use or application, all logical con- 
clusions must be reconverted into grammatical 
propositions, or, in other words, construed as 
asserting not merely the significative relation 
expressed, but also the truth or reality of the 
notions or concepts denoted by the terms; and 
when thus construed the conclusion cannot be 
regarded as being absolutely true, unless the 
terms express real notions. Hence, it may be 
said that the conclusions reached in ratiocina- 
tion proceeding exclusively from judgments 
are, when construed grammatically, true only 
upon the hypothesis that the notions involved 
in the original judgments or premises are true 
or real, and hence, that such conclusions are 
true absolutely only as logically construed. 
Thus, e, g,, the judgment that ** all bodies 
are affected by gravity*' is intuitive; but of 
the truth or reality of the notions expressed 
by these terms, respectively, we have no as- 
surance but experience. And from these ob- 
servations it may be perceived how, and in 
what sense, it is that Politics, Morality, and 
the Science of Human Nature generally are 
all to a large extent susceptible of demonstra- 
tion, and to that extent apodictic in their nature 
(§§ 23 et seq.\ 



CHAPTER IV 

DOCTRINE OF THE SYLLOGISM 

I 

RUDIMENTS OF THE DOCTRINE 

§ 73. Elements of the Syllogism. — The 
Syllogism consists of three propositions (§ 22) : 
of which two are called the prejniseSy and the 
other the conclusion. It has also three terms. 
Of these, two appear as the subject and the 
predicate of the conclusion, and are called, 
respectively, the minor and the major term. 
The other — which is called the middle term — 
is used in both premises: in the one with the 
"major ^ in the other with the minor term. The 
premise containing the major term is called 
the major, and that containing the minor, the 
minor premise. Thus in the syllogism, *' Y is 
X, Z is Y, .-. Z is X," Z is the minor, X the 
major, and Y the middle term ; and the first 
proposition the major, and the second the 
minor premise. 

74 



THE SYLLOGISM 75 

§ 74. Analysis of the Syllogism. — The 
proposition is but the expression of a signifi- 
cative relation between its terms. Hence the 
premises of a syllogism are merely statements 
of the significative relations of the terms of 
the conclusion (the major and the minor) re- 
spectively with the middle term ; and the 
conclusion the significative relation thereby 
inferred between its terms. The essential ele- 
ments of the process consist, therefore, in the 
comparison of the two terms of the conclusion 
respectively with the third, or middle term, 
and in inferring a direct relation between them. 

§ 75. Definition of the Syllogism. — 
Hence syllogistic inference may be more 
specifically defined as consisting in the infer- 
ence of a significative relation between two 
terms from their known significative relations 
to a third term with which they are respectively 
compared.^ 

§ j6. The Principle of the Syllogism. 
— The principle of the syllogism (by which is 
meant the principle or axiom on which de- 
pends the illative force or conclusiveness of 
syllogistic inference) is expressed in th^ Dictum 
of Aristotle, or, as it is technically called, the 

^ The definition in the text is taken substantially from that 
of De Morgan ; who defines the syllogism as " the inference 
of the relation of two names from the relation of each of those 
names to a third" (Formal Log. ^ p. 176). 



^6 LOGIC 

Dictum de Omni et Nullo. It is variously 
stated by logicians, but the several forms are 
all, in effect, identical. Its best expression is 
as follows : 

DICTUM DE Omni et Nullo.— '' Where 
three terms (which we will call the middle 
and the two extremes) so subsist with re- 
lation to each other that the one extreme is 
contained in the middle, and the middle is 
contained in [or excluded from^ the other ex- 
treme, then [as the case may be] the extreme 
included in the middle will be included in [or 
excluded from?^ the other extreme.** * Where 
the predication is affirmative the principle is 
called the Dictum de Omni ; where negative y 
the Dictum de Nullo, 

Omitting in the form given above the words 
in brackets, it becomes the Dictum de Omni ; 
substituting the words in brackets, marked as 
quoted, for the corresponding expressions, it 
becomes the Dictum de Nullo, 

The two forms of the Dictum (affirmative 
and negative) correspond precisely to the two 
forms of syllogisms called Barbara and Cela- 
renty^ viz. : 

^ This is substantially the form given to the Dictum by 
Aristotle, Prior Analytics, i., iv. 

^ Forms of the Syllogism. There are nineteen forms of 
valid syllogisms recognized by logicians, which are explained 
in the next chapter. But if we reject the use of particular 
propositions (§ 52 n.) all may be reduced to the two forms 



THE SYLLOGISM yy 



YisX 


Y is not X 


Zis Y 


Z is Y 


ZisX 


.'. Z is not X 



II 

THE PRINCIPLE OF SUBSTITUTION 

§ yy. Rules of Inference.— The follow- 
ing practical rules may be deduced from the 
Dictum : 

(i) In any affirmative proposition we may 
always (without affecting its illative force or 
conclusiveness) substitute for the subject any 
other term denoting the same, or part of the 
same, significates; and for the predicate any 
term denoting the same significates, or a class 
that contains them. 

Or, more briefly, we may always in the sub- 
ject substitute species for genus ; and in the 
predicate, genus for species. 

(2) So, in any negative proposition, we may, 
without affecting its illative force, substitute 
for either subject or predicate any term denot- 
ing the same, or part of the same, significates. 

Or, more briefly, we may always, in the 
negative proposition, either in the subject or 
the predicate, substitute species iox genus. 

above given, vv^hich are called Barbae' a and Celarent. In 
these forms the several terms may be represented indifferently 
by any letters ; and the order of the propositions is imma- 
terial. In the traditional Logic the order of the propositions 
is always as in the examples given in the text. 



78 • LOGIC 

(3) To which may be added the following: 
In any afifirmative proposition we may always 
substitute for the predicate any other term that 
denotes the same significates as the subject, or 
a class containing them/ 

§ 78. Equivalence of Terms Defined. 
— In the above rules, it will be observed, the 
term substituted is not necessarily equivalent 
in signification to the term for which it is sub- 
stituted ; but it is equivalent so far as the 
force of the inference is concerned, or, as the 
lawyers say, quoad the argument. It may be 
said, therefore, briefly, that mediate^ or syllo- 
gistic inference consists simply in substituting 
for the terms of propositions other terms equiv- 
alent in ratiocinative value. 

§ 79. Conversions of Propositions. — 
The case of conversion of propositions seems 
indeed, to be an exception ; for here the pro- 
cess seems to consist, not in the substitution 
of terms, but in the substitution of a new 

^ The deduction of these rules from the Dictum is perhaps 
sufficiently obvious, but as it may not be apparent to all, we 
subjoin the demonstration : 

In the first syllogism {Bai^bard) it will be perceived, as ex- 
pressed in the minor premise, that Z is a species, and X the 
genus, of Y, and that the conclusion is arrived at by substitu- 
ting for Y, in the major premise, its species Z ; or, for Y in the 
minor premise, its genus X. 

In the latter syllogism {Celarent) the process consists in sub- 
stituting for Y, in the major premise, its species Z ; and so it 
is obvious we may substitute for X in the major premise any 



THE SYLLOGISM 



79 



proposition containing the same terms as the 
original with the order of terms transposed. 
But the exception, in the case of negative and 
equational propositions, is more apparent than 
real ; for the two forms of the proposition (/. ^., 
th.Q co7tverted diwd the original proposition) are 
precisely the same in effect, and there is, in 
fact, neither term nor proposition substituted. 
For when we say ** Y is not X,*' we equally 
and as explicitly say '* X is not Y " — the mean- 
ing of either proposition being simply that the 
two classes denoted by X and Y are mutually 
exclusive; and so in the equational proposition 
(Y = X) we say, in the same breath, both that 
Y is equal to X, and that X is equal to Y. So, 

species of the genus X, as, e. g,, A, B, or C, and thus con- 
clude that " Z is not A, B, or C " (as the case may be) ; as may 
be illustrated by appropriate diagrams : 





So, in the major premise in Barbara, we may substitute for 
X the expression YX, or any species of X containing Y, as, 
e. g., A, and thus conclude that Z is YX, or Z is A, as the 
case may be. 




80 LOGIC 

upon consideration, it will be found that the 
conversion of the (universal) affirmative propo- 
sition — /. e,y conversion /^r accidens — is not an 
exception to the rule, but an application of it; 
for the process consists simply in substituting 
for the predicate another term precisely equiv- 
alent to the subject in signification, as, e, g,y 
in the proposition ** Y is X,'' the expression 
** some X" for ** X," — meaning, by the ex- 
pression ** some X," that part of X which co- 
incides with Y; which is but an application of 
Rule 3. And when this substitution is made, 
the proposition becomes equational, and means 
the same thing whether we convert it or 
not. 

§ 80. Of Immediate Inferences Gener- 
ally. — Propositions derived from other propo- 
sitions by conversion, and also those derived 
by opposition (explained infrUy § 89), are re- 
garded by recent logicians as inferences, and 
to distinguish them from syllogistic inferences 
are called immediate. This innovation we re- 
gard as unfortunate, though of too general use 
to be neglected, for, according to our view, 
only one kind of inference is allowed, namely, 
syllogistic. This, as we have shown, includes 
the case of conversion /^r accidens ; and it also 
includes other, and perhaps all, cases of so- 
called immediate inference ; as may be readily 
shown. 



THE SYLLOGISM 8 1 

(i) Substitution of Contradictory. — 
One of these is what is called by Bishop 
Thompson, ** Immediate Inference by Means 
of Privative Conceptions^'' and by other logi- 
cians, improperly, '' Infinitationy It is, in fact, 
identical with the process treated hereafter 
under the head of ** Conversion by Contrapo- 
sition " (§ 91). It consists in substituting for 
the predicate its negative, or contradictory, and 
in changing the quality of the proposition, — 
/. ^., making the copula of the negative propo- 
sition affirmative, or that of the affirmative 
proposition negative. Thus, denoting the 
terms by the capital letters Y and X, and their 
negatives or contradictories by aY and aX, 
the negative proposition ** Y is not X '' may be 
converted into the affirmative proposition, *' Y 
is aX '* ; and similarly the affirmative proposi- 
tion, ** Y is X,'* into the negative proposition, 
** Y is not aX ^^ (/. ^., is not Not-X). The 
validity of the process, as may be illustrated 
by the following diagrams, rests upon the prin- 
ciple that any negative proposition, as, e, ^., 
** Y is not X,'' may always be regarded either 
as denying that the class Y is included in the 
class X, or as affirming that it is included in 
the class aX, or *' Not-X''; and conversely 
the affirmative proposition, ** Y is X,'* may 
be regarded either as affirming that the 
class Y is included in the class X, or as 



82 



LOGIC 



denying that it is included in the class aX, 
or'^ Not-X/^ 






But when from the affirmative proposition 
** Y is X '" we conclude that *' Y is not Not- 
X," there is a syllogistic inference; which, de- 
noting the negative or contradictory of X by 
aX, may be thus expressed : 

X is not aX (/. <?., not Not-X) 
YisX 
/. Y is not aX. 

The inference, therefore, rests upon the 
judgment that the term '' X " is equivalent to 
the term ** Not-aX,'' and consists in substi- 
tuting the latter for the former. Hence the 
principle of inference involved may be stated 
generally by saying that a term is always 
equivalent in signification to the contradictory 
of its contradictory y or, as otherwise expressed, 
the negative of its negative ; which is but a 
different expression of the maxim that ** two 
negatives make an affirmative/' 

It is, indeed, said that the major terms in the 
two propositions are the same — the proposi- 
tions differing only in quantity, and hence 



THE SYLLOGISM 83 

that no third term is introduced. But this is 
incorrect ; for the major term in the former 
proposition is X, and in the latter ** not 
Not-X " ; and it is a fundamental logical doc- 
trine that no two terms are identical that differ, 
either in denotation or connotation, or vocal 
sign; and also that, the very essence of ratio- 
cination consists in the recognition of identity 
of signification in terms having different con- 
notations or vocal signs, and in the substitution 
of the one for the other (§§ j"] et seq,), 

(2) Immediate Inference by Added De- 
terminants, AND (3) THE Same by Complex 
Conceptions. — These kinds of supposed im- 
mediate inference were introduced into Logic 
by Leibnitz (Davis, Theory of Thought, p. 104). 
The former is stated in the proposition that the 
same mark may be added to both terms of a 
judgment; the latter, in the proposition that 
the two terms of a judgment may be added to 
the same mark. Of the former, the example 
given by Thompson is: ** A negro is a fellow- 
creature," therefore, ** A negro in suffering is 
a fellow-creature in suffering " ; of the latter: 
** Oxygen is an element,*' and therefore, ** The 
decomposition of oxygen would be the decom- 
position of an element.'* The two processes 
seem to be in substance the same, and both 
may be expressed symbolically by saying that 
'' If Y is X,*' then** ZY will be ZX,'* or (what 



84 LOGIC 

is the same) '' YZ will be YX " ^ ; as may be 
thus symbolically illustrated; 




This process is erroneously regarded by logi- 
cians as an immediate inference; but it is, in 
fact, mediate^ and may be stated in syllogistic 
form as follows : 

Y is X 

ZY is Y 

/. ZY is X 

The conclusion *' ZY is X,** fully expressed, 
is that ZY is that part of X with which it co- 
incides; or, in other words, that ** ZY is ZYX/* 
But ZYX is ZX; and hence ZY is ZX. 

In this case the observations made with 
reference to infinitation {supra) will apply a 
fortiori; for here a new term, '' ZY,*' is in- 
troduced, differing from Y in denotation, in 
connotation, and in verbal sign. 

^ But the converse is not true, — i. e., from the proposition, 
ZY is ZX, we cannot infer that Y is X ; as will appear from 
the following diagram : 




THE SYLLOGISM 85 

It may therefore be concluded, as already 
asserted, that all inference consists in sub- 
stituting, for terms of propositions, other terms 
of equivalent ratiocinative value. 

§ 81. Formal and Material Substitu- 
tions. — Substitution of terms may be either 
formal or material. The former includes all 
cases where the substituted term is the original 
term in a modified form, — as, where the ele- 
ments of a complex term are arranged in a dif- 
ferent order, as, e. g,^ where YX is substituted 
for XY; or, as where the original term is 
qualified by some other word or words express- 
ing a formal relation existing between the sub- 
stituted term and the original, — as, e. g,, where 
in the proposition ** Y is X," we substitute for 
** Y'^** some Y,'^ or for '* X*' '' notNot-X''; 
or, as in the example given above, where we 
substitute for ** negro " and ** fellow-creature'* 
the terms *' negro in suffering " and '' fellow- 
creature in suffering.'* Material substitutions 
are those where a new term is substituted, as, 
e. g.y where we substitute for a term a syno- 
nym, or species for genus, or genus for species. 

Ill 

OF MATHEMATICAL REASONING 

§ 82. Mathematics the Type of all 
Ratiocination. —Hence it would seem that 



86 LOGIC 

the most perfect type of ratiocination is pre- 
sented by the mathematical, and especially by 
the algebraic methods of demonstration ; and 
this is, in fact, the case, as may be illustrated 
by two familiar examples: 

1st Example, Thesis, — The angles of a plain 
triangle are together equal to two right angles; 
or, referring to the figure, a -f- t) -f- c = yK 
(Euclid, Book I., Prop. XXXII.). 




For 

a + b' + c' = A {lb,, Prop. XXIX.). 

But 

b' = b 
c' = c. 

Hence, substituting equivalents, 

a + bV+ c' =: a + b + c —Ai.. Q. E. D. 

2d Example, Thesis, — The formula for com- 
pound interest, ^. ^., S = p (1 -|- r)", in which 
p = principal, n = number of years, r = rate 
of interest, and S =:: the amount. 

At end of first year 

S ::= p + pr = p (1 + r). 

At end of second year 

S = p (I + r) + pr (1 + r) r= p (1 + r)«. 



THE SYLLOGISM 8/ 

At end of third year 

S = p (1 + ry + pr (1 + rr = p (1 + r)\ 

At the end of n years 

S = p (1 + x)\ 

% 83. A Current Error on this Point. 
— It is indeed asserted by recent logicians that 
there is an essential difference between ordinary 
and mathematical^ or, as it is otherwise ex- 
pressed, between qualitative and quantitative 
reasoning. But this opinion arises from the 
failure to reflect that the comparison of magni- 
tudes can be effected only by means of units of 
measurement that can be applied equally to 
the magnitudes compared, and that these con- 
stitute the significates denoted by mathemati- 
cal terms. Hence mathematical reasoning 
consists not in directly comparing the magni- 
tudes considered, but in comparing the units 
that represent them ; and mathematical terms 
must therefore be regarded as denoting — like 
other terms — collections or classes of individ- 
uals, /. ^., of the units expressed. 

An Opinion of Mr. Bain. — On this point 
we have the following from Mr. Bain: ** Logi- 
cians are aware that the form * A equals B, B 
equals C, therefore A equals C ' is not reducible 
to the syllogism. So with relation to * greater 



88 LOGIC 

than* in the argument a fortiori ; yet to the 
ordinary mind these inferences are as natural, 
as forcible, and as prompt as the syllogistic 
inference/' But the first expression is a per- 
fect syllogism differing from the ordinary form 
only in the different interpretation given to the 
copula; and this is true also of the argument 
a fortiori^ if we give it the form, ** A < B, 
B < C .*. A < C* It is strange this is not 
recognized by the author; or, rather, would be 
strange were not the error common. What 
is meant, therefore, is that the mathematical 
cannot be reduced to the ordinary form of the 
syllogism. But this is not the case, for mathe- 
matical reasoning can readily be expressed in 
the ordinary logical forms, as, e. g,, the equa- 
tional syllogism in the two syllogisms follow- 
ing: 

a is b ^ - b is a 

b is c c is b 

.'. a is c .*. c is a; 

and the argument a fortiori in the following: 
** a is b, b is c, .". a is c,** — meaning that the 
class of units denoted by a is contained in the 
class denoted by b, etc. 

Or the inequalities may be converted into 
equations, as, ^. ^. ,* ' a < b ' ' into * * a -[- x == b, * * 
and the argument then be expressed in two 
syllogisms as above. 



the syllogism 89 

§ 84. Reduction of Euclid's Fifth 
Proposition to Syllogisms. — Recognizing 
the mathematical form of the syllogism, there 
is no need of the cumbersome method usually 
adopted for the reduction of mathematical 
reasoning to syllogistic form, as, e. g,, in the 
ancient example of the reduction of Euclid's 
Fifth Proposition given by Mansel in his notes 
to Aldrich ; or the reduction of the same prop- 
osition by Mill {Logic, p. 142). 

In fact, Euclid's demonstration is itself in 
syllogistic form, and needs only a slight varia- 
tion in the statement of it to make this ap- 
parent, as, e, g,y as follows: 

Prop. V. The angles at the base of an 
isosceles triangle are equal to one another. 

Or, referring to the figure, in the isosceles 
triangle ABC the angles a and c are equal. 

The figure is constructed by 
producing the equal sides A B 
and A C to D and E, making 
the lines A D and A E equal, 
and by drawing the lines B E 
and D C. 

Demonstration 

1ST SYLLOGISM 

Major Premise. — Prop. IV. 

Minor Premise. — The triangles ABE and 




90 LOGIC 

A C D are triangles having two sides of the one 
equal to two sides of the other, each to each, 
and the included angle equal. 

Conclusion, — They are therefore equal in all 
their corresponding parts, and hence B E = 
C D and the angle d = the angle e. 

2D SYLLOGISM 

Major Premise. — Prop. IV. 

Minor Premise. — The triangles C B E and 
BCD are triangles having two sides of the one 
equal to two sides of the other, each to each, 
and the included angle equal. 

Conclusion. — They are therefore equal in all 
their corresponding parts, and hence the angle 
f = the angle g. 

3D SYLLOGISM 

Major Premise, a — d — f. (Judgnnent, or 
intuitive proposition.) 

Minor Premise, d -^ f = e — g. 
Conclusion, a = e — g. 

4TH SYLLOGISM 

Major Premise, a = e — g. 
Minor Premise, e — g = c. 
Conclusion^ a = c. 



CHAPTER V 

SUMMARY OF THE TRADITIONAL LOGIC 

I 



OF THE TRADITIONAL LOGIC GENERALLY 

§ 85. As explained in the preface, one of 
the principal objects of this work is to vindi- 
cate, as against modern innovations, the old or 
traditional Logic; and accordingly, in all that 
has been said — with exceptions to be noted 
presently — I have kept close to the traditional 
view, as expounded by Aristotle and the most 
approved of the older logicians. I have, in- 
deed, repudiated the doctrine advocated by 
Whately, and by modern logicians generally, 
that would distinguish between the forma/ sind 
the material relations of terms, and restrict the 
scope of Logic to the former; but in this also 
I follow Aristotle and the better authorities. 

The only particulars, therefore, in which I 
have departed from the traditional view of 
Logic are: (i) that I reject the ** Particular 
Propositions '* of the old Logic and those parts 
of the old doctrine of the Proposition and of 

91 



92 LOGIC 

the Syllogism that are founded on this view 
of the proposition ; and (2) that I have adopted, 
in place of the Dictum, the Principle of Sub- 
stitution ; which is an obvious corollary from 
the Dictum, and is more readily understood 
and applied. 

At the same time, it must be admitted, the 
old doctrines of the Proposition and the Syl- 
logism are remarkable for the accurate analysis 
upon which they rest, and the wonderful ingen- 
uity and acuteness with which they have been 
developed. They have thus become part of 
the accepted philosophy of the world ; and there 
has thus been developed a technical language 
that has come to be universally received and so 
generally used that, without an understanding 
of it, all the literature on the subject must be 
a closed book to us. I now propose, therefore, 
to give a brief exposition of these doctrines. 

II 

THE TRADITIONAL DOCTRINE OF THE PROPOSITION 

§ 86. QUALTITY OF PROPOSITIONS. — Prop- 
ositions are said to differ in quality accord- 
ingly as they are affirmative or negative. Thus 
the propositions *' All Y is X " and ** Some 

Y is X " are affirmative ; the propositions ** No 

Y is X " and ** Some Y is not X," negative. 

§ 87. Quantity of Propositions. — Again, 
propositions, whether affirmative or negative, 



TRADITIONAL LOGIC 



93 



are said to differ in quantity accordingly as the 
predicate is asserted, or denied universally of 
all individuals of the class denoted by the sub- 
ject or only part of such individuals. In the 
former case the subject is said to be distributed, 
and the proposition is called universal ; in the 
latter, the subject is undistributed, and the 
proposition is said to be particular. Thus, 
e. g.y the propositions, ** All Y is X** and 
** No Y is X '' are both universal; and the 
propositions, ** Some Y is X '' and '* Some Y 
is not X," both particular. 

§ 88. Table of Propositions.— Hence, 
four forms of propositions are recognized by the 
old logicians, viz. : (i) the Universal Affirma- 
tive ; (2) the Universal Negative ; {^) iht Par- 
ticular Affirmative ; and (4) the Particular 
Negative ; which are designated respectively 
by the letters A, E, I, and O; and, with their 
expressions in Euler's Symbols, are as fol- 
lows, viz. : 

A: YisX(/. ^., All YisX) 

E: Y is not X (/. e,, No Y is X) ^ (7) (7) 

I: Some YisX (vox: 




O: Some Y is not X Q^j^ 

* The above differs somewhat from the ordinary notation ; 



94 LOGIC 

In the negative propositions, E and O, it 
will be observed, the predicate is distributed or 
taken universally; in the affirmative proposi- 
tions it is undistributed. 

§ 89. Opposition of Propositions. — Two 
propositions are said to be opposed to each 
other when, having the same subject and pred- 
icate, they differ in quantity or quality, or both. 

Propositions that differ both in quality and 
quantity, as A and O, or E and I, are called 
contradictories^ as, ^. ^., ** Y is X," and ** Some 

Y is not X '^ or ** Y is not X '^ and '' Some 

Y is X.** Those that differ in quality only, if 

according to which it is thought necessary in A and E to use 
the signs " All " and " No," in order to indicate that the sub- 
ject is distributed, as, e, g., "All Y is X," "No Y is X." 
But, properly speaking, the signs "All" and " No" are un- 
necessary and redundant. For when we say, e. g,, ""Man is 
mortal^'' or " Ma7i is not mortal,'' we mean, when we speak 
properly, that in the former case the class "man" is ivholly 
included in, and in the latter that it is wholly excluded from, 
the class "mortal" ; or, in other words, as the case may be, 
that '''All men are mortal,'' or that ''No man is mortal" 
(§ 53, n.). The last expression is also objectionable on ac- 
count of the liability to confound the expression " No man " 
with the term " Not-man " in converting either of the above 
propositions by contraposition (for which see infra, § 91) ; 
or (more generally) the negative proposition "No Y is X " 
is liable to be confounded with the affirmative proposition, 
"" Not-Y is X." Hence it will be preferable to regard the 
subject as always distributed, except where it is preceded by 
the adjective " some " ; and, in place of the sign " no" before 
the subject, to use the particle " not" after the copula. 



TRADITIONAL LOGIC 



95 



universal, are called contraries, as, ^. ^., ** Y is 
X '' and ** Y is not X '' ; and if particular, sub- 
contraries y as, e, g,y ** Some Y is X " and 
** Some Y is not X/' Where propositions 
differ in quantity only, as A and I, or E and 
O, the particular propositions are called subal- 
terns , diSy e, g.y ** Y is X " and ** Some Y is 
X ''-, and '' Y is not X " and '' Some Y is 
notX/' 

There are, therefore, four kinds of opposition 
recognized by logicians, viz. : (i) the opposi- 
tion of contradictories ; (2) that of contraries ; 
(3) that of subcontrarieSy and (4) that of subal- 
terns to their corresponding universals; which, 
with their relations to each other, are admi- 
rably expressed in the following table, which 
has come to us from ancient times: 



■CONTRARY' 



X 



X 



/ 



A 



fp 



^\i 



■SUBCONTRARY- 



(i) Contradictories. The most complete 
kind of opposition is that of contradictories. 
These cannot both be either true or false : /. ^., 
if one is true, the other is false ; or, if one is 



96 LOGIC 

false, the other is true. For if it be true that 
** All men are sinners/' it cannot be true that 
** Some men are not sinners '' ; and, conversely, 
if it be true that ** Some are not righteous/' it 
cannot be true that ** All men are righteous/' 
In other words, between contradictories there 
is no intermediate proposition conceivable; one 
must be true and the other false. This is 
called the law of Excluded Middle. 

(2) Contraries. Contraries cannot both 
be true; for if it be true that *' Every man is 
an animal," it must be false that ** No man is 
an animal." But both may be false, as, for 
example, the propositions that ** All men are 
learned," and that ** No men are learned"; 
which are both false, for some are learned and 
some are not. In other words, contrary propo- 
sitions do not exclude the truth of either of the 
particular propositions between the same terms. 

(3) SUBCONTRARIES. Subcontraries are con- 
trasted with contraries by the principle that 
they may be both true, but cannot both be 
false. Thus it may be true that ** Some men 
are just," and also that ** Some men are not 
just " ; but if it be false that ** Some men are 
just," it must be true that ** No man is just," 
— which is the contradictory y — and, a fortiori, 
that '*Some men are not just," — which is the 
subcontrary. 

(4) SUBALTERNATE OPPOSITION. With tC- 



TRADITIONAL LOGIC 97 

gard to subaltern propositions, their truth 
follows from the corresponding universal pro- 
positions; forif ** all men are animals," ** some 
men are animals," and if ** no man is an ape," 
** some men are not apes." But from the truth 
of a subaltern proposition we cannot infer the 
truth of the corresponding universal, as, e, g\y 
from the proposition ** Some men are false,'* 
the proposition ** All men are false "; or from 
the proposition ** Some men are not false," the 
proposition that ** No man is false." 

§ 90. Observations upon Contrary and 
Contradictory Oppositions. — Accurately 
speaking, these constitute the only kinds of 
opposition. Siibcontraries are, in fact, not op- 
posites ; and the same is true of siibalterns and 
their corresponding universals. 

It will be observed it does not follow from 
the principle of contrary opposition that of 
two terms regarded as subject and predicate — 
as, e, g,^ Y and X — either the latter or its 
negative may always be predicated of the 
former, or, in other words, that Y must be 
either X, or not X ; for, in fact, some Y may 
be X, and some Y not X, as will obviously 
appear from the following diagrams : 




©0 



98 LOGIC 

.Hence there arises, seemingly, a puzzling 
contradiction between this principle and the 
law of Excluded Middle — as it is often stated. 
Thus, it is said, ** Rock must be either hard or 
not hard'' (Jevons, Lessons in Logic, p. 119), 
or, generally, " Y is either X or not X." But 
obviously this, unless accidentally, is not true; 
for some rock may be hard and some soft ; or 
some Y may be X, and some not X. And so 
we cannot say of ** men '' either that they are 
learned or that they are not learned ; for some 
are the one and some the other. But the ap- 
parent contradiction arises from the misstate- 
ment of the law of Excluded Middle; which 
is itself nothing more or less than the principle 
governing contradictories, as expressed above. 
We may, indeed, where a subject term (as, 
e, g,y Y) denotes an individual or single thing 
(real or fictitious), affirm of it that it is either 
X or not X; but if Y denotes a class of more 
than one we cannot so affirm.^ 

' Even Hobbes falls into the error of Jevons on this point. 
"Positive and negative terms," he says, "are contradictory 
to one another, so that they cannot both be the name of the 
same thing. Besides, of contradictory names, one is the name 
of anything whatsoever {i. e., of any conceivable thing), for 
whatsoever is, is either a man^ or not a man, white, or not 
white, and so of the rest." But, it may be asked, " Does the 
name 'biped' denote (universally) either man, or not man?" or 
" the name 'man', either white man, or man not white?" 

The confusion results from the technical view that regards 



• TRADITIONAL LOGIC 99 

§ 91, Conversion of Propositions. — A 
proposition is said to be converted when its 
terms are transposed, i, e,, when the subject is 
made the predicate and the predicate the sub- 
ject (§ 54). Such conversion is admissible 
only when illative, i. e,, where the truth of the 
converse is implied in that of the original prop- 
osition. When such conversion can be made 
without otherwise changing the proposition it 
is called a simple conversion ; otherwise, it is 
called 2, zoviv^x^xow per accidens. Thus A (** Y 
is X ") cannot be converted simply, because the 
subject only is distributed; we therefore can- 
not say that ** All X is Y,'* but only that 
** Some X is Y,** which is called conversion per 
accidens. But E ('* Y is not X *') — as both sub- 
ject and predicate are distributed — may be con- 
verted simply ; or, in other words, we may say 

the Particular Proposition as a form distinct from the Uni- 
versal, and its source would be removed if, as elsewhere 
suggested, this form of the proposition should be rejected 
(§ 52, n.). We might then adopt, as equally accurate 
and profound, the remaining observation of Hobbes, that 
" the certainty of this axiom, namely, that of two contradic- 
tory names one is the name of anything whatsoever, the other 
not, is the original and foundation of all ratiocination, that 
is, of all philosophy " {Logic, Sec. 8), which is in accord with 
the view of Aristotle : " For the same thing to be present and 
not to be present, at the same time, in the same subject, and 
in the same sense, is impossible. . . . For by nature this 
is the first principle of all the other axioms" (Metaphysics, 
R. iii,, chap. iii.). 



100 LOGIC 

that " No X is Yr So with I C* Some Y is 
X'*),^ — as both subject and predicate are un- 
distributed, — the proposition may be simply 
converted, i, e,, if *' Some Y is X/' then it is 
necessarily true that ** Some X is Y/' 

By one or the other of these methods, i. e., 
either simply ox per accidenSy all propositions of 
the forms A, E, and I may be converted. But O 
C' Some Y is not X '') cannot be thus converted. 
Thus, e, g,y it cannot be inferred from the prop- 
osition ** Some Greeks are not Athenians'' 
that ** Some Athenians are not Greeks." But 
such conversion may be effected by simply re- 
garding the negative particle (not) as part of 
the predicate ; by which expedient O is changed 
into I, and may be simply converted, as, e, g,, 
** Some Greeks are Not-Athenians *' ; which 
may be converted into the proposition ** Some 
Not-Athenians are Greeks. ' * So from the prop- 
osition ** Some men are not learned,'' though 
we may not infer that *' Some learned are not 
men," we may infer that ** Some unlearned 
are men." This is called by the old logi- 
cians ** Conversion by Contraposition^'' and by 
Whately, ** Conversion by Negation,'' 

This method of conversion is applicable to 
A and E as well as O, and, as it is of very ex- 
tensive use, we append a table of such conver- 
sions, taken, with some alterations, from De 
Morgan {Formal Logic, p. 6j), In this table 




TRADITIONAL LOGIC lOI 

(altering De Morgan's notation) the original 
terms of the proposition are denoted by the 
capital letters Y and X, and their contraries 
respectively by prefixing the Greek privative a. 
We append also for illustration the symbolical 
expressions for the several propositions: 

A: ^^ Y is X " ; ** Y is not aX " ; '' aX is not Y " ; 
" aX is aY " : 



The righteous are happy ^ 

The righteous are not unhappy ,' 

The unhappy are not righteous *^ 
The unhappy are unrighteous. 



E: "Yisnot X"; ^^YisaX"; *^ Some aX is Y " ; 
'' Some aX is not aY." 

" X is not Y " ; ** X is aY " ; " Some aY is X " ; 
" Some aY is not aX " : 

Perfect virtue is not human '^ u \ 

Perfect virtue is unhuman {{^\ V^*i 

Some unhuman virtue is perfect yvj/-- v^i 

Some unhuman virtue is imperfect. \ • 

Human virtue is not perfect 
Human virtue is imperfect 
Some imperfect virtue is human 
Some imperfect virtue is not unhuman. 

O: '' Some Y is not X " ; " Some Y is aX " ; " Some 
aX is Y " ; '' Some aX is not aY " : 



/ 


u 


"S 


^K 


/ 


/O^ 


r\ 


\ 
\ 


( 


( Y n 


M 




\ 


v^y 


J 


/ 


\ 


^f^ 




/ 



102 LOGIC 

Some possible cases are not probable 

Some possible cases are not improb- 
able 

Some improbable cases are possible 

Some improbable cases are not im- 
possible. 

It will be observed from the above table that 
a universal affirmative proposition can always 
be converted into another universal affirmative 
between the contradictories of its original terms 
by simply reversing the order of the terms and 
substituting for them their contradictories. 

§ 92. Of Material Conversions. — It will 
be observed that the conversions of propositions 
treated by logicians have regard to the dis- 
tinction, heretofore explained, between the 
formal and the material relations of terms 
(§ 66 (2)), and are confined exclusively to what 
may be called/(?r;;/^/ conversions, i. ^., to cases 
where the equivalence of the converted and 
original propositions results from th.^ formal or 
general relations of terms. But conversions of 
propositions based upon the material relations 
of terms are of essentially the same nature, as, 
e, g,, where the proposition ** John is the son 
of William '* is converted into the proposition 
** William is the father of John**; or the 
proposition ** Cain murdered Abel ** into the 
proposition ** Abel was murdered by Cain,** or 
into the proposition '' Cain is the man that 



TRADITIONAL LOGIC I03 

murdered Abel." These, having regard to 
the received distinction between the formal 
and the material relations of terms, may be 
called ;;^^^^r/^/ conversions ; and are infinitely 
the more numerous class, and equally deserv- 
ing of attention. But though conversions of 
this kind are in constant use, and though, in- 
deed, we cannot proceed a step in our logical 
processes without them, yet the subject has 
received but little attention, and remains as 
yet a vast, unexplored domain.^ It can only 
be said, therefore, in the present condition of 
logical doctrine, that as the distinction be- 
tween t\\^ formal d^ndi the material x^X'dAXoxis of 
terms has been found unessential, so must the 
distinction between formal and material con- 
versions be regarded. Both classes of conver- 

* To this domain belong such subjects as the "'Categories,^'' 
''''Intensive Propositions,'" '' Hypothetical Propositions,''' and, 
in short, all forms of expression that differ from the ordinary- 
logical proposition. With these Logic is concerned only in 
so far as is involved in their conversion into logical forms. 
Otherwise, neither the Intensive nor the Hypothetical Logic 
(if we may give either the name) can be regarded as part of 
Logic as traditionally received ; which is based exclusively 
upon the logical form of the proposition and its extensive 
interpretation. With regard to the Hypothetical Logic, it 
will be observed, it has no place in Aristotle's treatises ; and 
Mansel is of the opinion — in which I agree — that in this he 
showed a juster notion of the scope of Logic than his suc- 
cessors. The subject is well treated in the current works on 
Logic, and is worthy of some attention from the student. 



104 LOGIC 

sions rest equally for their validity simply 
upon judgments as to the equivalence of ex- 
pressions. 

Ill 

THE TRADITIONAL DOCTRINE OF THE SYLLOGISM 

§ 93. The following epitome of the doctrine 
of the syllogism as traditionally received, brief 
as it is, will — with what has already been said 
— be found amply sufficient to expound it. 
It will, indeed, require the same close attention 
and thought as is usually given to mathemati- 
cal demonstrations; but it may be said that 
to those who are unwilling to give, or are in- 
capable of giving, to it this kind of thought, 
the study of Logic cannot be of much benefit. 

I . Of the Moods and Figures of the Syllogism 

§94. Moods of the Syllogism. — The syl- 
logism is said to be in different moods, according 
to the occurrence and arrangement in it of the 
several forms of the proposition — A, E, I, and 
O; as, e. g,, in the syllogism ** Y is X, Z is 
Y, .*. Z is X,*' which consists of three universal 
affirmative propositions, and is, therefore, said 
to be in the mood AAA. 

The four forms of the proposition. A, E, I, 
O, may be arranged, in sets of three each, in 
sixty-four different ways, but upon examina- 
tion it is found that of these there are eleven 



TRADITIONAL LOGIC 105 

arrangements only that constitute valid syllo- 
gisms; and hence the legitimate syllogism can 
have but eleven moods, viz. : 

Table of Moods 

A A A, A A I, A E E, A E O, A I I, 
A O O, E A E, E A O, E I O, I A I, O A O. 

§ 95. Figures of the Syllogism.— Again, 
syllogisms are said to be of different figures, 
according to the position of the middle term in 
the syllogism with reference to the extremes ; 
and as there are said to be four different ways 
in which the middle term may be thus placed, 
syllogisms are said to have four figures, viz. : 
the 1st figure, where the middle term is the 
subject of the major and the predicate of the 
minor premise ; the 2d, where it is Xht predicate 
both of the major and of the minor premise; 
the 3d, where it is the subject of both the major 
and the minor premise ; and the 4th, where it 
is th.Q predicate of the major and the subject of 
the minor premise. Thus — using the conven- 
tional symbols — the forms of the different 
figures are usually expressed as follows : 





Table 


of Figures 




1st Fig. 


ad Fig. 


3d Fig. 


4th Fig. 


Y X, 


X Y, 


Y X, 


X Y, 


Z Y, 


Z Y, 


Y Z, 


Y Z, 


Z X, 


Z X, 


Z X, 


Z X. 



I06 LOGIC 

If the eleven moods of the syllogism were all 
valid in each of the four figures, there would 
result forty-four different kinds of syllogisms 
differing in mood or figure. But none of the 
moods are valid in all the figures; and it is 
found on examination that there are in fact 
only twenty-four kinds of syllogisms that are 
valid; and that of these five are useless. So 
that the number of different kinds of legiti- 
mate syllogisms recognized by logicians is 
nineteen. 

§96. Reduction of Syllogisms. — All 
these forms may, however, be reduced or con- 
verted — without affecting their validity — into 
the form of the first figure; which is accord- 
ingly regarded by logicians as the principal, or 
7iormal figure of the syllogism. The different 
figures and moods of the syllogism, and the 
methods of reduction or conversion from one 
figure to another, are briefly expressed in the 
following hexameter verses, constituting what 
may be called 

The Table of Syllogisjns 

Fig. I — Barbara, Cd^r^nt, Daru\ Fm^que, prioris 
Fig. 2 — Cesare, C^m^str^s, Yestino, Fakoro, secundae 
Fig. 3 — Tertia, D<^r^pt/, D/s^m/s, DaU'si, Felapton, 

DokamOy Feriso, habet, quarta insuper 

addit 
Fig. 4 — Bramantip, C^m^n^s, D/m^r/s, Yesapo, 

Fresison, 



TRADITIONAL LOGIC 10/ 

In these lines the words commencing with 
capital letters (except ** Tertia *') are the names 
of the several syllogisms in each figure, and 
the italicized vowels point out the moods of 
the propositions constituting the several syl- 
logisms. Thus, e. g.y the vowels indicate that 
Barbara consists of the three propositions, A, 
A, A; Celarent of E, A, E; Darii oi A, I, I; 
Feriso of E, I, O, etc. 

The initial letter in the name of each syllo- 
gism in the second, third, and fourth, or, as 
they are called, the indirect figures, indicates 
that the given syllogism is to be reduced to the 
syllogism in the first figure commencing with 
the same letter, as, e, g.y Cesare, Camestres, 
Camenes into Celarent ; Bramantip into Bar- 
bara ; Daraptiy etc., and Diinaris, etc., into 
Darii ; Fe^tino, etc., Felapton, etc., diVid Fesapo, 
etc., into Ferio. 

The letters s, /, and k indicate that the pro- 
position indicated by the vowel immediately 
preceding is to be converted — s indicating 
simple conversion, / conversion per accidens, 
and k conversion by contraposition , or nega- 
tion,'^ 

^ The use of conversion by contraposition as a means of 
reduction is a late invention. It is, in general, used only in 
the two forms, Fakoro and Dokarno, — or, as they were origi- 
nally called, Baroko and Bokardo, — as all other forms can be 
reduced without its aid, i. e., by the use of simple conversion 
or conversion /^r accidens. Prior to the use of this method, 



I08 LOGIC 

The letter m indicates that the premises are 
to be transposed. 

The other letters are without significance. 

Table of Syllogisms. By the use of the 
'' Table of Moods" and the '' Table of Fig- 
ures/' all the syllogisms given in the '* Table 
of Syllogisms *' may be readily constructed, 
and the mode of reducing the syllogisms in the 
second and third and fourth figures to the cor- 
responding syllogisms in the first figure be 
readily perceived.* 

Baroko and Bokardo could not be directly reduced to the first 
figure, but indirectly only by a process called reductio ad 
i?npossible ; which consisted in substituting for one of the 
premises the contradictory of the conclusion. 

By this method Baroko is converted into a syllogism in Bar- 
bara, having the contradictory of the original conclusion for a 
minor premise, and the contradictory of the original minor 
premise for a conclusion, which, as the minor premise is true 
ex hypothese, is an absurdity, viz,^_ 

(Original Syllogism) (Reduced Syllogism) 

Xis Y XisY 

Some Z is not Y Z is X 

.•. Some Z is not X .*. ZisY 

By the same method Bokardo is converted into a syllogism 
in Barbara, having the contradictory of the original conclusion 
for a major premise, and the contradictory of the original 
major for a conclusion, e, g. : 

Some Y is not X Z is X 

Yis Z YisZ 

.' . Some Z is not X / . Y is X 

^ A table of the several syllogisms, with their reductions, 
illustrated by Euler's symbols, is appended (see Appendix M). 



traditional logic io9 

§ 97. Observations upon the Forms of 
Syllogisms. — It will be observed from what 
has been said that the numerous forms of syl- 
logisms recognized by the old logicians result 
from two assumptions — the one erroneous and 
the other unnecessary. 

The first is the erroneous assumption that 
the symbols Y and X must always be taken as 
denoting respectively the 7ninor and the major 
terms; from which results that there 2S^ four 
figures of the syllogism, instead of three. But 
if in the fourth figure we regard X as the minor 
term and Y as the major, it becomes of the 
first figure. Hence the fourth figure — which 
was not recognized by Aristotle, but is a late 
invention — is rightly rejected by the best 
authorities. 

The other assumption is that the particular 
propositions {** Some Y is X ** or ** Some Y is 
not X *') are to be regarded as involving the 
same terms as the universal (** Y is X '* or ** Y 
is not X *'), and the expression ** some *' as a 
mere sign of quantity; from which (and the 
first assumption) there result the four forms of 
the proposition. A, E, I, and O, and the nine- 
teen forms of syllogism recognized by logicians, 
Barbara, Celarent, etc.^ 

* The doctrine of the syllogism, and especially that of its 
moods and figures, has been elaborated by the logicians per- 
haps to an unnecessary extent, but as it stands must always 



no LOGIC 

% 98. Proposed Simplification of 
Forms. — But if in X^xo, particular propositions 
(I and O) we regard the expression ** some '* 
not as a sign of quantity, but as part of the 
term, — or, in other words, if we regard ** Some 
Y'* instead of *' Y'* as the term,— they be- 
come the same as *' A " and '' E," i, e.y Univer- 
sal (§ 52, n.). By this simple change the four 
forms of the proposition are reduced to two (A 
and E), and the nineteen forms of syllogism to 
the two simple forms of Barbara and Celarent.^ 

2. Of the Dictum de Ojnni et Nullo 

§ 99. Of the Several Forms of the 
Dictum. — The principle of the syllogism, or 
the Dictum de Omni et Nullo, has already been 
considered at length, and what has been said is 
sufficient to elucidate its nature. It is, how- 
ever, variously stated by logicians, as indeed 
by Aristotle himself, and it will be of interest 
to consider some of its various forms. 

constitute a necessary part of a liberal education. For prac- 
tical use, however, it is unnecessarily complicated ; and it will 
be found that when modified, as we have suggested {i. e., by 
rejecting the particular proposition, and substituting for the 
ordinary form of the dictum the Principle of Substitution), 
the simplicity of its application will be largely increased. 

^ More accurately, perhaps, it should be said to four forms, 
namely, Barbara, Celarent, Cesar e, and Camestres. But the 
last two are essentially the same as the second, and there is no 
advantage to be gained by distinguishing them. 



TRADITIONAL LOGIC III 

Of these, in addition to the form already 
given, and which is on all accounts to be pre- 
ferred, there are two others to which we will 
refer. 

These, as given by Whately, are as follows : 

** Whatever is predicated \i, e,, affirmed or 
denied] universally of any class of things, may 
be predicated in like manner [viz., affirmed or 
denied] of anything comprehended in that 
class " {Logic y bk. i., § iv.). 

** Whatever is predicated of a term dis- 
tributed, whether affirmatively or negatively, 
may be predicated in like manner of everything 
contained under it ''{Id,, bk. ii., chap.iii., §2). 

In effect, these two statements may be taken 
as types of all the other forms of the dictum. 
But, as we have observed, '* thing'' or ''things " 
is an extremely vague and unsatisfactory term, 
and it would be better to substitute for it the 
expression ** significate," or ** significates/* 

These two forms of the dictum are in ef- 
fect the same. For to say, as in the latter, 
^'Whatever is predicated of a term distributed,'* 
is in effect to say, '' Whatever is predicated 
universally of any class,'* etc. Bearing this 
in mind, and substituting ** significates " for 
** t kings y" both forms of the dictum may be 
more briefly expressed by saying that ** a term 
predicated of a term may be predicated also of 
any or all of its significates.'* Where the pred- 



112 LOGIC 

ication is affirmative the principle, as we have 
seen, is called the Dictum de Omni ; where it 
is negative, the Dictum de Nullo. 

It is said by Whately that the dictum *' can- 
not be directly or immediately applied to all 
even categorical syllogisms, but, as all syllo- 
gisms may be reduced to the first figure, it may 
be ultimately applied to all/' Hence, ** to 
avoid the tediousness of reducing all syllogisms 
to that form to which Aristotle's dictum is ap- 
plicable, it has been deemed necessary to in- 
vent separate rules or canons for the indirect 
figures'' (Whately, Logic, bk. ii., chap, iii., § 2); 
and in this logicians generally agree. 

§ 100. Canons of the Several Figures. 
— These canons of the several figures — omitting 
the fourth figure, which is disallowed by the 
best authorities as being a mere perversion of 
the first — are as follows: 

First Figure : The Dictum de O^nni et Nullo, 
as above. 

Second Figure: Dictuin de Diver so. If one 
term is contained in and another excluded from 
a third term, they are mutually excluded. 

Third Figure : Dictum de Exemplo, Two 
terms which contain a common part, partly 
agree, or, if the one term contain a part which 
the other does not, they partially differ (Devey's 
Logic, pp. 109-111). 

§ loi. The Dictum, Rightly Expressed, 



TRADITIONAL LOGIC I13 

Applicable to All the Figures.— But if 
the form of the dictum we have adopted, and 
which is substantially as given by Aristotle 
(§ l^y be taken, it will be found to apply to 
all syllogisms universally. But as the form 
given in the paragraph cited has reference to 
the division of propositions there adopted into 
two kinds only (namely, A and E, rejecting I 
and O), it must now be stated somewhat differ- 
ently, so as to apply to the ordinary division 
of propositions into their four kinds. A, E, I, 
and O : 

** Where three terms (which we will call the 
middle and two extremes) so subsist with rela- 
tion to each other that the one extreme is in- 
cluded {wholly or partly) in the middle, and 
the middle is included in or excluded from the 
other, then (as the case may be) the extreme 
included in the middle will be {wholly ox partly) 
included in or excluded from the other ex- 
treme.*' 

Or dividing the proposition, and leaving the 
terms ** wholly '* or ''partly '* to be supplied 
as required, it may be stated thus : 

Dictum de Omni: (a) If one extreme of a 
syllogism be included in the middle and the 
middle in the other extreme, then will the 
former be included in the latter. 

Dictum de Nullo : (b) If one extreme of a 
syllogism be included in the middle^ and the 

8 



1 14 LOGIC 

middle be excluded from the other, then will the 
former extreme be excluded from the latter. 

In this form the dictum may be readily ap- 
plied to each of the three figures. 

With regard to the first this is sufficiently 
obvious; for the syllogisms in this figure are 
in fact but mere symbolical expressions of the 
dictum — ^that is to say, Barbara and Darii of 
the Dictum de Omni, and Celarent and Ferio 
of the Dictum de Nulla. 

With regard to the second figure, \h^ Dictmn 
de Nulla is, in effect, identical with the Dictum 
de Diver so. For to say, as is said in the former, 
that ** the middle term is excluded from the 
last extreme,** is in effect to say, ** that ex- 
treme is excluded from the middle'*; and 
hence the Dictum de Nulla agrees with the 
Dictum de Diversa in asserting that two terms, 
the one of which is included in and the other 
excluded from a common middle term, are 
mutually excluded. 

So in the third figure the dictum is equally 
applicable. For in the affirmative forms {Da- 
raptiy DisamiSy and Datisi) it is asserted that 
the middle is contained in, and in the negative 
forms {Felapton, Dakamo, and Feriso) that it 
is excluded from one of the extremes; and in 
both it is asserted, in effect, that the other ex- 
treme is partly included in the middle. Hence 
the former come directly under the Dictum de 



TRADITIONAL LOGIC II5 

Omni, and the latter under the Dictum de 
Nullo, 

That the dictum agrees with the Dictum de 
Exemploy however, cannot be said; for that, in 
terms, merely asserts the truism that ** two 
terms which contain a common part '* in that 
respect agree, or, ** if one contain a part 
which the other does not,'* to that extent 
differ. But it gives us no information as to 
the principle by which it is determined 
whether the two terms have or have not a 
common part. Whereas the dictum of Aris- 
totle explains that if one extreme be partly 
included in the middle, and the middle be 
either wholly included in or excluded from the 
other extreme, then the two extremes will or 
will not agree or have a common part, as the 
case may be. 

It is therefore obvious that the dictum of 
Aristotle applies equally to all syllogisms, and 
that to invent separate canons for the several fig- 
ures is unnecessary and productive of confusion. 

§ 102. The Dictum Applicable to Sing- 
ular AND OTHER EQUATIONAL PROPOSI- 
TIONS.- — It has also been objected to the 
dictum by several logicians that it is not ap- 
plicable to syllogisms in which the terms are 
singular, or to other syllogisms composed of 
equational propositions; which, it is said, are 
governed by a different regulating principle, 



Il6 LOGIC 

viz., that ** notions equivalent to one and the 
same third notion are equivalent to each 
other'' (McCosh, Logicy pp. 126, 127). But 
this is obviously not so. For an individual 
may, for logical purposes, be regarded as a 
class {i. e,y a class of one); and classes that are 
equal to each other mutually include each 
other. Hence the dictum applies directly to 
syllogisms of this character; and we may al- 
ways express such a syllogism, e, g,y Z = Y, 
Y = X .*. Z = X, in the usual form: Z is Y, 
Yis X .-. Zis X. 

§ 103. Of Proposed Improvements on 
THE Dictum. — Other objections are urged to 
the dictum of Aristotle by modern logicians, 
and, to remedy its supposed defects, numerous 
new dicta or canons have been invented to take 
its place. But these will be found on examina- 
tion to be either erroneous or merely different 
and less satisfactory statements of the old 
dictum. 

In at least this fundamental aspect of the 
subject the opinion of Kant with reference to 
the Old Logic must be accepted, viz., that 
'* Since Aristotle it has not had to retrace a 
single step, and to the present day has not 
been able to make one step in advance.'' ^ 

^ In these views I find myself supported by the following 
judicious observations of Professor Jevons : 

*' During the last two or three years," he observes, "the 



TRADITIONAL LOGIC II7 

3. Rules of the Syllogism 

% 104. Statement of the Rules. — The 
following rules, with the fallacies resulting from 
their violation, are given by logicians. They 
are all obvious deductions either from the 
definition of the syllogism or from the dictum 
of Aristotle. 

(i) Every syllogism has three, and only 
three, terms, viz., the Major, the Minor, and 
the Middle term. 

The violation of this rule is called the Fal- 
lacy of Four Terms {Quarternio Terminorum), 
It generally results from the ambiguity of a 
term, and indeed can hardly occur in any 
other way. 

(2) Every syllogism contains three, and only 
three, propositions, viz., the Major and the 
Minor premise and the Conclusion. 

This rule can be violated only by violating 
the first rule, and is therefore to be regarded 
as superfluous. 

(3) The Middle term must be distributed 
once at least in the premises. 

thought has constantly forced itself on my mind, that the 
modern logicians have altered the form of Aristotle's proposi- 
tion without making any corresponding alterations in the 
dictum or self-evident principle, which formed the fundamen- 
tal postulate of his system. Aristotle regarded the proposi- 
tion as stating the inclusion of one term or class within 
another ; and his axiom was perfectly adapted to this view 
{Pure Logic, p. 86). 



Il8 LOGIC 

The violation of this rule is called the Fallacy 
of Undistributed Middle, as, e, g,, in the fol- 
lowing pseudo-syllogism: X is Y, Z is Y .*. Z 
is X. 

(4) No term must be distributed in the con- 
clusion that was not distributed in one of the 
premises. 

The violation of this rule is called the Fallacy 
of the Illicit Process of the Major or of the 
Minor term, as the case may be, as, e. g,y in 
the following syllogism : Y is not X, some 
Z is Y .•. Z is not X, — Nations capable 
of self-government should not be despotically 
governed; some nations are capable of self- 
government ; no nation should be despotically 
governed, — which is a case of illicit process of 
the Minor term ; or as in the following syllo- 
gism: Y is X, Z is not Y .*. Z is not X, — 
Anglo-Saxons love liberty, Frenchmen are 
not Anglo-Saxons .*. Frenchmen do not love 
liberty, — which is an illicit process of the Major. 

(5) From negative premises nothing can be 
inferred. 

The violation of this rule is called the Fallacy 
of Negative Premises; e, g,y Y is not X, Z is 
not Y .*. Z is X or Z is not X. 

(6) If one premise be negative the conclusion 
must be negative ; and, vice versa, to prove a 
negative conclusion one of the premises must 
be negative. 



TRADITIONAL LOGIC II9 

The violation of this rule may be called the 
Fallacy of Afifirmative Conclusion, e,g,, Y is 
X, Z is not Y .-. Z is X. 

And from the above rules may be deduced, 
as corollaries, the following: 

(7) From two particular premises no conclu- 
sion can be drawn. 

(8) If one premise be particular, the conclu- 
sion must be particular. 

4. Of Enthymemes and Sorites 

§ 105. Of Enthymemes.— An Enthymeme 
is a syllogism incompletely stated, but in 
which the omitted parts are understood or im- 
plied. Most commonly the omitted part is the 
major premise, which is then said to be sup- 
pressed, as, e, g,y ** Caesar was a tyrant, there- 
fore he deserved death," where the suppressed 
premise is the major, ** All tyrants deserve 
death.'' Or the suppressed premise may be 
the minor, as, e, g., '* Freemen are happy, 
therefore the English are happy,'* where the 
suppressed premise is the minor, ** English- 
men are freemen." 

§ 106. Of Sorites. — The Sorites consists of 
a string of syllogisms in the first figure, in 
which the conclusion of each is made the 
premise of the next, and so on, till finally in 
the conclusion the predicate of the last premise 



I20 LOGIC 

IS predicated of the subject of the first, as, 
e. g,, K is B, B is C, C is D, D is E . *. A is E ; 
or, to give a concrete example, ** The English 
are brave, the brave are free, the free are 
happy, therefore the English are happy/' 
Obviously a Sorites may always be resolved 
into as many separate syllogisms as it has 
middle terms, as, e, g.y in the above example, 
the first into three and the last into two syllo- 
gisms, as follows: 



A is B 


A is C 


A is D 


B is C 


C is D 


D is E 


A is C 


.-. A is D 


.-. A is E 



The English are brave The English are free 
The brave are free The free are happy 

The EngHsh are free /. The English are happy, 




BOOK II 
APPLIED LOGIC 



131 



BOOK II 



APPLIED LOGIC 



PART I 



OF THE METHOD OF LOGIC 



CHAPTER VI 



OF THE LOGICAL PROCESSES 



§ 107. Of the Method of LoGic.^The 
logical processes, as we have hitherto con- 
sidered them, consist in three operations, 
namely. Simple Apprehension, Judgment, and 
Syllogism or Inference; of which the first is 
an analytical process, the second and third 
synthetical. Hence the logical processes may 
be regarded as twofold, and as consisting in 
Analysis and Synthesis. The first of these, 
however, is not confined to Simple Apprehen- 

123 



124 LOGIC 

sion or analysis of terms, but extends to the 
analysis of propositions and syllogisms, and of 
extended discourse ; of which the elements are 
syllogisms. It also extends, as preparatory to 
the expression in logical form of subjects to be 
investigated, to the analysis of the general 
facts involved and the determination of the 
questions to be investigated. The logical 
method consists in the use of these processes. 
§ io8. Logical Distinguished from 
Physical Analysis and Synthesis. — The 
terms analysis and synthesis are used in differ- 
ent senses, according to the subject-matter to 
which they are applied. Of these, two princi- 
pal kinds may be distinguished, which may be 
called, respectively, physical and logical — the 
former dealing with physical substances, the 
latter with notions or concepts. Of the former 
kind, the most instructive illustration is pre- 
sented by chemistry ; where these processes are 
applied directly to matter, which is analyzed 
by separating its elements, and synthesized by 
rearranging those elements so as to form new 
compound substances. These processes are 
indeed essentially different in nature from the 
processes with which we are now concerned, 
yet the analogy between the two is almost 
perfect; and hence, in chemical analysis and 
synthesis, we find the best illustration of the 
nature of analysis and synthesis of notions or 



THE LOGICAL PROCESSES 1 25 

terms, by which — in a way very similar to the 
analysis and synthesis of material bodies — 
notions are analyzed into elementary notions, 
and these again synthesized into compound. 

§ 109. Of the World of Things and 
THE World of Thought. — The world of 
things is made up of actual things or sub- 
stances; the world of thought, of concepts or 
notions. There is between the two a regular 
correspondence, i, ^., a correspondence deter- 
mined by invariable law, and yet the two are 
clearly distinct. For it is obvious that things 
themselves cannot be in the mind but only, 
notions or concepts of them. These, as we 
have seen, if real or true, must correspond, 
either directly or indirectly, with the things 
which, or the attributes of which, they are 
supposed to denote (§ 29, n.). Where the 
correspondence is indirect, the thing denoted 
is a quasi-thmg only, and cannot be distin- 
guished from the notion itself; but where the 
correspondence is direct, there is a real thing 
corresponding to the notion, and we may 
either regard the notion or the thing as the 
significate of the term (§ 37, n.); though even 
in this case it is really the notion, not the 
thing, that we have in mind (§ 38, n.). So 
that it may be said that Logic, and science 
generally, deal directly with concepts or no- 
tions only — that is to say, with the world of 



126 LOGIC 

thought only, and with the world of real things 
only indirectly. 

§ no. Logic as the Doctrine of Signs 
(SemeiOTIKE). — But the notions or thoughts 
dealt with by Logic are not the evanescent 
thoughts of the in*dividual, but the common 
notions of mankind embodied in language 
(§ 30). Hence, as we have observed. Logic 
is exclusively conversant with language, or 
rather, more specifically, with terms and their 
various ratiocinative combinations (§§ 14, 16) 
— that is to say, with the signs of the notions 
or concepts and of their relations ; which 
cannot be dealt with, at least to any con- 
siderable extent, except by means of the 
vocables by which they are signified. Hence 
Logic must be regarded, in its direct scope, as 
dealing with the signs by which notions and 
their relations are expressed — precisely as, in 
the mathematics, the subject-matter dealt with 
consists of the signs of numbers and of their 
relations. In both cases, therefore, though 
the ultimate object of Logic is to determine 
the notions expressed in terms and their re- 
lations, and ultimately the nature and the 
relations of the things corresponding to the 
notions, yet this is effected by means of signs, 
which, therefore, constitute the immediate 
subject dealt with. Hence Locke was quite 
right in conceiving that a science of this char- 



THE LOGICAL PROCESSES 12/ 

acter is indispensable, and in giving it the ap- 
propriate name of ** Semeiotikey or the Doctrine 
of Signs," though quite wrong in supposing 
that this would be a new kind of Logic* 

§ III. The Method of Logic Resumed. 
— By the method of Logic is meant the method 
of its use in reasoning, or, in other words, the 
method of ratiocination, or explicit reasoning. 
This, as we have said, consists in two processes 
or operations, namely. Analysis and Synthe- 
sis, i, e,y of language (§ 107). By analysis is 
meant the separation of a whole — whether con- 
sisting of a term, proposition, syllogism, or 
larger discourse, or of the general problem 
or subject to be investigated — into its com- 
ponent parts ; by synthesis, the comparison (or 
placing together) of any of the elements of 
reasoning, with a view to determining their re- 
lations; that is to say, in the comparison of 
terms, in order to form a judgment of their 
relations — of propositions, in order to make an 
inference; and of syllogisms, in order to make 
an extended ratiocination or argument. An- 
alysis and synthesis are, therefore, each the 
converse of the other. 

§ 112. Modes of Application of the 

^ ** The consideration then of ideas and woj'ds, as the great 
instruments of knowledge. . . . Perhaps if they were 
distinctly weighed and duly considered, they would afford us 
another sort of Logic and critic than what we have hitherto 
been acquainted with " (see Appendix N). 



128 LOGTC 

Logical Processes. — In each stage of ratio- 
cination analysis and synthesis are used con- 
jointly, and each is equally indispensable. The 
order in which their applications occur, how- 
ever, differs according to the purpose we have 
principally in view, which may be either In- 
vention or Criticism; that is to say, either (i) 
the Discovery of Truth, or (2) the Criticism or 
Judgment of what is supposed or alleged to be 
true; or, in other words, the verification of 
truth and the detection of fallacy. Of these 
two aspects of Logic, the latter is commonly, 
and perhaps rightly, regarded as the more im- 
portant, or, at least, as of the greater practical 
utility. But the former, though commonly 
undervalued, is hardly of less utility or less 
fruitful of practical results. 

§ 113 (i) Invention. — The operations of 
Logic, regarded as an Instrument or Organon 
of Invention, consist in the analysis and conse- 
quent apprehension of terms (Simple Appre- 
hension), and in the discovery or invention of 
judgments and of syllogisms, and of argu- 
ments — which are composed of syllogisms; 
which is effected by synthesis; and the process 
of ratiocination proceeds in this order, i, e,, 
from the term to the proposition, from the 
proposition to the single syllogism, and from 
that to the extended discourse or argument. 

§ 114. Of the Distinction between 



the logical processes 12$ 

Original and Commonplace Thought. — 
Where the notions expressed in terms are dis- 
tinctly apprehended, and, with reference to all 
terms, to the extent they are apprehended, the 
relations between them are readily perceived, 
and indeed spontaneously present themselves. 
Hence with such notions men reason with 
facility and accuracy; and thus originate the 
numerous opinions that are common to man- 
kind, or common at least to men generally 
under the same conditions of environment; 
and also those that are common to large classes 
of men. Of such opinions — which may be ap- 
propriately named Commonplace — the current 
literature and thought of the day largely, or, 
we may say almost exclusively, consist. Hence 
the effect of current thought and discourse 
is simply to disseminate such opinion more 
widely, and thus gradually to develop and 
consolidate Common Opinion, or Conscience, 
which has been called by the Greeks Nomos^ 
and by some philosophers Common Sense. 
This, indeed, is a useful and essentially neces- 
sary function ; for it is recognized by political 
writers generally that opinion is the ultimately 
controlling force in politics, and that when it 
becomes universal and inveterate, it is supreme. 
But current thought is marked by an essential 
characteristic, or, we may say, defect — namely, 
that it is incompatible with originality, either 



130 LOGIC 

in the acquisition of new truths or in the ap- 
preciation of original thought in others. Hence 
it has happened, throughout the history of 
mankind, that the results of original thought 
meet with almost insuperable obstacles to their 
reception ; and that, even where they have es- 
tablished their footing, they pass into the 
hands of commonplace thinkers, who treat 
them after their own methods. Hence the 
original works of great thinkers, with their 
methods of thought and expression, and the 
vivifying effect of actual example, are sub- 
merged by the newer and inferior literature. 

On the other hand, where the Analytical 
Method is rigorously applied to all forms of 
discourse, and especially when it is applied to 
the notions or concepts embodied in terms, 
numerous delicate and important but unsus- 
pected relations between the notions thus de- 
termined suggest themselves. For in this also 
logical is like chemical analysis, where, 
by the resolution of compound substances, 
thousands of relations between them and 
between the elements of which they are 
composed are developed and disclosed. The 
perception of these unsuspected relations con- 
stitutes originality^ which is but another name 
for logical power. Nor is this originality any- 
where more conspicuously displayed than 
where men of original genius, as, e. g., Bacon 



THE LOGICAL PROCESSES 13I 

in his Essays, deal with commonplace subjects/ 
Hence the use of Logic as an Instrument of 
Invention cannot be too highly appreciated, 
for in the capacity to use Logic in this way, 
or, in other words, in the capacity to apprehend 
the whole significance of terms by resolving 
them into their elements, lies the essential dif- 
ference between the Original and the Common- 
place Thinker.* 

§ 115 (2) Criticism. — In this aspect Logic, 
may be likened to the touch of IthurieFs spear.'*; 

* Where terms are clearly defined and analyzed into their 
constituent elements, — that is to say, thoroughly apprehended y. 
— innumerable relations between them are intuitively per- 
ceived ; and thus, by the use of this method, we are led on, 
as Locke says in a passage cited {supra § 6, n.), "from 
very plain and easy beginnings, by gentle degrees and a con- 
tinued chain of reasonings, ... to the discovery and 
demonstration of truths that appear, at first sight, beyond 
human capacity." This it v/as, probably, that inspired the 
beautiful hymn of Newman : 
"Lead on, Heavenly Light; amid the encircling gloom, 

Lead Thou me on " ; 
which may be very properly regarded as in reality an ode to 
the divine gift of Intuition — the only source of perfect 
knowledge. 

^ " Him there they found 
Squat like a toad at the ear of Eve. 



Him thus intent Ithuriel with his spear 
Touched lightly ; for no falsehood can endure 
Touch of celestial spear, but returns 
Of force to its own likeness ; . . . 
So started up in his own shape the fiend," 



132 LOGIC 

Commonly the reasoning processes operate 
unconsciously and automatically, and the rea- 
soning is more or less inaccurate, and hardly 
ever consecutive or logically coherent. As 
observed in the Introduction, proposition fol- 
lows proposition in our minds, suggested by 
various principles of association, such, e. g., as 
experience, habit, authority, inclination, etc. ; 
and thus the great mass of our opinions and 
beliefs— which we very erroneously call our 
knowledge — comes to us we know not how. 
Nor, however firmly we may be convinced of 
them, or however passionately we may assert 
them, have we any just assurance of their 
truth; nay, it is matter of familiar knowledge 
that they are all mingled with error. Hence, 
we concluded, the necessity is apparent for 
some test or criterion by which to judge them ; 
and this, except the sometimes painful test of 
ocperience, can be nothing else than Logic. 
In its critical aspect, therefore, Logic is indis- 
pensable, not only to save us from errors and 
absurdities, but to distinguish real from unreal 
knowledge, and to give us assurance of the 
former (§ 7 et seq.). Without it, except in 
concrete matters, no man can know whether 
he is right or wrong; and while some, happily 
born, learn by practice the application and 
use of the logical processes, the great mass of 
mankind, for the lack of Logic, go through life 



THE LOGICAL PROCESSES 1 33 

mistaking falsehood and even nonsense for 
knowledge, and yet firmly convinced of their 
wisdom and of the folly of those who differ 
from them. Hence, in the critical aspect of 
Logic, the order of applying the logical pro- 
cesses is the reverse of what it is in the use of 
Logic as an organon or instrument of inven- 
tion. There the order is to commence with 
the analysis of the term, and then to proceed 
to the synthesis of terms in propositions, 
syllogisms, and extended discourse; here we 
commence with the complex result, and by 
analysis resolve it into its elements. 

§ 116. Of the Use of Analysis Gener- 
ally. — In the use of Logic, whether for in- 
vention or for criticism, analysis and synthesis 
are equally indispensable; but the latter, after 
the former has been effected, is largely a 
natural and spontaneous process, and presents 
but little difficulty in its performance. On the 
other hand, analysis, while to a certain extent 
also spontaneous, requires, for its efficient per- 
formance, the most vigorous and protracted 
exertion of the mental faculties, — as, e.g,, in 
the mathematics, — and hence is at once the 
most important and the most difficult of the 
logical processes. It will therefore require 
our special attention. 

We have distinguished between the inven- 
tional diXid the critical functions of Logic, and 



134 LOGIC 

also with reference to the use of the logical 
processes as applied in the performance of the 
one or the other function ; and with reference 
to invention, we have regarded the function of 
analysis as limited to the analysis of terms, 
with a view to an apprehension of the notions 
expressed by them. In practice, however, it 
is difificult to distinguish between the uses of 
analysis for invention and for criticism. For, 
as we have observed, the human mind is so 
constituted that the synthetical process is 
performed spontaneously and involuntarily. 
Hence there is no subject that can present 
itself for our investigation which we can ap- 
proach unembarrassed by opinions already 
formed; and, indeed, until such opinions or 
theories are formed, the process of investiga- 
tion cannot commence. Hence, as is generally 
recognized, the method of scientific investiga- 
tion must consist largely in the forming of 
theories and their subsequent investigation. 
We may distinguish, however, between our 
own theories, either accidentally formed or 
formed for the purpose of the investigation of a 
proposed subject, and the theories formally pro- 
pounded by others, either in writing or speech ; 
and we may conveniently regard the former as 
belonging to the function of invention, and the 
latter to that of criticism. The latter, as being 
the simpler subject, will be first considered. 



THE LOGICAL PROCESSES 1 35 

§ 117. (i) Of the Use of Analysis in 
Criticism. — In this case the function of 
analysis extends to the analysis of all forms 
of language, from the term to the extended 
discourse or argument; and, as we have ob- 
served, it commences with the latter, which is 
in fact the most difficult task. For here it is 
necessary to determine from the loose and in- 
accurate expressions of ordinary disquisition 
the precise nature of the conclusions asserted 
and of the arguments used to establish them ; 
and this task is always difficult, and sometimes 
impossible. When these matters have been 
determined it will be necessary also to analyze 
carefully every syllogism, proposition, or term 
involved in the course of the reasoning. But 
this in general, to the trained logician, presents 
but little difficulty. 

§ 118. (2) Of the Use of Analysis in In- 
vention. — Strictly speaking, this perhaps ex- 
tends only to the analysis of the term with a 
view to simple apprehension, and in a previous 
passage we have so regarded it. But before 
this task can be approached, it is necessary for 
us to determine the nature of the precise ques- 
tions to be investigated ; and this will require an 
analysis of the facts involved in the investiga- 
tion, and also of the opinions or theories with 
regard to those facts casually existing in the 
mind. For, as will be explained more fully in 



136 LOGIC 

the next chapter, the questions demanding in- 
vestigation are in general determined by the 
nature and the conditions of the problems 
involved ; and it is essential to a rational in- 
vestigation that the issues thus involved be 
clearly ascertained. When the issues or ques- 
tions are thus determined and logically ex- 
pressed, our investigation is then narrowed to 
the determination of the truth of one of two 
alternative propositions, which are called the 
thesis and the anti-thesis, and of which one or 
the other must be true; and thus our task is 
in general greatly facilitated. The use of this 
sort of analysis finds its best illustration in the 
practice of the lawyers, with whom it is an im- 
perative rule that the first step in the investi- 
gation of a case must consist in settling the 
issues. In ordinary discourse this task is 
almost always neglected, and, as will be seen 
as we proceed, this is one of the most fruitful 
sources of fallacy. 

§ 119. Of Analysis and Synthesis Gen- 
erally.— This subject is one of extreme im- 
portance, and to the advanced student should 
constitute one of the principal subjects for his 
meditations; but for the purposes we have in 
view it may be sufficiently developed by a 
statement of the practical rules by which the 
reasoner should be governed, which will be 
given at length in the next chapter. 



CHAPTER VII 

THE RULES OF LOGIC 

I 

OF THE RULES OF LOGIC GENERALLY 

§ I20. Scope of the Rules of Logic. — 
According to the view we have taken in this 
essay, inference is only one of the processes of 
ratiocination. Judgment is also a ratiocinative 
process, and, Hke inference, must have its rules 
by which false or pretended judgments may be 
distinguished from the real. Moreover, where 
our reasoning is not apodictic, we have to use 
assumed propositions, or assumptions, as prem- 
ises; and though it is said that Logic is not 
concerned with the truth or falsity of these, yet 
this is true only in a qualified sense. For 
where the falsity of such propositions can be 
detected by logical processes, — /. ^., by defini- 
tion, judgment, and inference, — it is the func- 
tion of Logic to condemn and reject them; 
precisely as in the case of self-contradictory 

137 



138 LOGIC 

propositions or propositions otherwise absurd 
on their face. And in all cases it is its func- 
tion to determine the logical character of an 
assumed premise, as being an assumption or 
hypothesis, and not a judgment. 

§ 121. Twofold Division of the Rules 
OF Logic. — We propose, therefore, to regard 
the rules of Logic as legitimately extending to 
all the processes of ratiocination ; and hence as 
including all rules necessary to direct us in the 
right use of terms as instruments of ratiocina- 
tion. They will include, therefore, not only 
the rules directly governing the process of in- 
ference, but also those governing the statement 
of the premises. The latter — which will first 
be considered^ — will be called the ** Rules of 
Judgment^'' the former, the '' Rules of In- 
ferencey 

§ 122. Rules of Judgment. — The rules of 
judgment have for their object, not the form- 
ing of rights but the prevention of wrong judg- 
ments. Judging is a natural and involuntary 
operation of the mind. But in the ordinary 
processes of the mind we are apt to go astray 
in our judgments; and the object of the rules 
of judgment is to guard against this infirmity 
by preventing false judgments, or, where they 
occur, by detecting them. 

8 123. Rules of Inference. — The rules 
of the syllogism given in a previous chapter 



THE RULES OF LOGIC 1 39 

cover all cases of inference except conversion 
per accidens. But these rules are needlessly 
complex, and may be advantageously replaced 
by the rules of substitution, which include 
all inferences whatever, and are simpler both in 
their expression and application than the old 
rules, of which they are but another expres- 
sion. The rules of the syllogism, however, 
are of such familiar use by logicians, and are so 
wrought into the terminology and literature of 
Logic, that a familiar acquaintance with them 
is essential to the logical student; for whom 
also it will be necessary to recognize clearly 
the substantial identity of the two processes. 

§ 124. Fallacies OF THE Syllogism, All 
Resolvable into Fallacies of Substitu- 
tion. — This is especially important with refer- 
ence to the violations of the rules of the 
syllogism, or, as they are called, the fallacies 
of the syllogism (§104 et seq\ These are 
of frequent occurrence, and are familiarly 
known by technical names; and as these have 
become firmly established in logical termi- 
nology by a use of many centuries, they must, 
of course, be retained. It will be of advantage 
to the student, therefore, to have pointed out 
to him that all these fallacies are simply cases 
of illicit substitution ; which can be readily 
shown. 

Thus, e, g.y the fallacy of an ambiguous 



140 LOGIC 

middle term {Qiiarternio Terminorum) consists 
simply in the substitution of a new term, hav- 
ing the same verbal sign as in the original, but 
a different meaning — as in the examples given. 

The case of undistributed middle — as, e. g,^ 
** X is Y, Z is Y .-. Z is X ^ — consists in the 
illicit substitution of species for genus in the 
predicate of an affirmative proposition (i. e.j X 
for Y in the minor premise). 

In the case of illicit process of the minor term, 
— as, e, g,, '* Y is not X, some Z is Y .*. Z is 
notX,*' — genus is illicitly substituted for species 
in the subject of an affirmative proposition 
{i. e.y Z ior *' Some Z '' in the minor premise). 

In the case of illicit process of the major ^ — as, 
e. ^., '' Y is X, Z is not Y .-. Z is not X,*'— 
genus is illicitly substituted for species in the 
predicate of a negative proposition (/. ^., X for 
Y in the minor premise)*^ 

In the case of negative premise, if the con- 
clusion be affirmative, — as, e, ^., *^ Y is not X, Z 
is not Y .•. Z is X,'' — genus is substituted for 
species in the predicate of a negative proposi- 
tion (/. ^., Not-X for Y in the minor pre- 
mise). If the conclusion be negative,' — as, e,g,, 
*' Y is not X, Z is not Y .-. Z is not X,^*— the 
fallacy will consist in the illicit substitution of 
one for another of two unrelated terms {i, e., 
X for Y); and the same will be true of the 
other cases, if any there be. 



THE RULES OF LOGIC I4I 

§125. The Laws of Thought. — The 
rules of Logic are founded upon what are 
called the primary Laws of Thought, viz. : 
(i) the Law of Identity (or rather the Law of 
Equivalence); (2) the Law of Contradiction; 
and (3) the Law of Excluded Middle; the first 
of which governs the process of Inference, the 
last two, that of the Judgment. The corre- 
sponding fallacies consist in their violation. 

These laws may be enunciated in a form to 
make them of practical utility, as follows: 

(i) The Law of Identity. 

Significates {i. ^., things or qiiasi-t kings) re- 
main the same though denoted by different 
terms. 

Hence terms denoting the same significates 
may, to the extent of their equivalence, be 
used interchangeably, /. ^., the one substituted 
for the other. 

The mathematical axiom that ** things equal 
to the same thing are equal to each other '* is 
merely a special application of this principle, 
its meaning being simply that terms denoting 
the same class of significates are equivalent to 
each other. 

It is obvious, therefore, that this law is not 
adequately stated (as is sometimes said) by the 
equation, A = A, but rather by the equation, 
A = B; both terms being supposed to denote 
the same class of significates, and the term B 



142 LOGIC 

to be either A, or any other vocable or sign 
denoting the same significates. 

(2) The Law of Contradiction, or 

RATHER THE LaW OF NON-CONTRADICTION. 

A term, and its 7iegative, or contradictory^ 
cannot be predicated universally of any term. 

This law and the next are often misstated. 

(3) The Law of Excluded Middle. 

Of two contradictory propositions, one must be 
true ; or symbolically : * ' Either A is B,'' or 
''Some A is not B.'' ' 

II 

RULES OF JUDGMENT 

§ 126. Rule I. Terms to be Significant. 

In every logical proposition — by which is meant 
every proposition to be used in ratiocination — the 
terms must be significant^ i, e,, must have defi- 
nite signification. 

This rule follows from the definition of the 
term and of the proposition ; for unless the 
word or vocable has such definite signification 
there is no name, and consequently no term or 
proposition, or valid ratiocination. The viola- 
tion of this rule may be called the Fallacy of 
Non-significance or Nonsense, 

Rule II. Terms to be Rightly Defined. 

Terms used in ratiocination must not only have 

* v., supra^ § 90. 



THE RULES OF LOGIC 1 43 

a definite signification^ but the signification 
must be legitimate^ i. e., they must not be falsely 
defined. This implies (i) that a term shall not 
be used in an improper sense ^ i, e, , ifi a sense not 
permitted by the usage of the language ^ ; and 
(2) that the ter^n shall be so defined as to signify 
a real concept ; or, at least, that the contrary 
shall not afiirmatively appear. 

The violation of this rule will be called the 
Fallacy of False Definition, 

Rule III. Premises not to be Illicitly 
Assumed. 

A proposition that is obviously untrue, or that 
can, on logical priitciples, be afiirmatively shown 
to be untrue, cannot be legitimately used as a 
premise. 

The violation of this rule is called the fallacy 
of *' Begging the Question/' or Petitio Prin- 
cipii ; and this and the fallacies resulting from 
the violation of Rules I. and II. may be 
classed together under the general head of 
Illicit Premises, 

Rule IV. Premises to Correspond to 
the Thesis or Issue. 

In all ratiocination — if designed to be fruitful 

^ The unnecessary use of a term in a sense not justified by 
usage is commonly indicative either of mental incapacity or 
fallacious intent ; and should therefore be forbidden, as to 
children we forbid the use of deadly weapons, or to all the 
possession of counterfeiters' tools. 



144 LOGIC 

— the premises^ and, consequently^ also the con- 
clusion^ must correspond to the Thesis or Issue^ 
zvhether that be expressed or understood, or 
merely determined by the conditions of the 
problem. 

By the thesis is meant the proposition to be 
demonstrated ; by the issue, the thesis and the 
anti-thesis, or contradictory, considered to- 
gether with a view of determining whether the 
one or the other is true. 

With regard to nearly all subjects presented 
to us for investigation the material question at 
issue is more or less definitely determined by 
the conditions of the problem ; and hence it is 
said, *' A prudent questioning is a kind of half 
knowledge " {Prudens interrogatio est dimidium 
sapientice). Where the issue is thus determined, 
it constitutes the real issue, or thesis and anti- 
thesis of the problem. In other cases it must 
be determined by agreement, or by actual in- 
tention, either expressed or understood. In 
many cases it is not formally stated, but we 
ascertain it, for the first time, from the use 
made of the conclusion. 

The fallacy resulting from a violation of this 
rule— if we assume there is no fallacy in the 
inference — will necessarily involve a departure 
from the thesis or issue, both in the premises 
and in the conclusion. With regard to the 
premises, it is called the fallacy of Mistaking 



THE RULES OF LOGIC I45 

the Issue ; with regard to the conclusion, that 
of Irrelevant Conclusion ; and in either case, 
Ignoratio Elenchi. 

Ill 

RULES OF INFERENCE 

§ 127. All inference, as we have observed, 
may be resolved into the process of substituting 
for terms other terms of equivalent ratiocina- 
tive value. There is an apparent exception in 
the case of conversions of propositions, but the 
exception is only apparent (§ 79). To conform 
to usage, however, the rule for conversion will 
be given, though in fact, as explained, the illicit 
conversion of a proposition is simply a case of 
illicit substitution of terms. 

Rule V. Conversions to be Illative. 

A conversion, to be legitimate , must be illative , 
i. e,, the truth of the converted must be implied 
in the original proposition. 

The violation of this rule may be called the 
Fallacy of Conversion, or simply Illicit Conver- 
sion. It can occur only in the simple conver- 
sion of a universal affirmative or a particular 
negative proposition (^. ^., ** Y is X,*' ** Some 
Y is not X **). In the former case the fallacy 
will consist in the substitution of genus for 
species (X for Y) in the subject, and of species for 
genus (Y for X) in XhQ predicate of a universal 



146 LOGIC 

afifirmative proposition, thus doubly violating 
the first rule of substitution. In the lat- 
ter (** Some Y is not X '') X is substituted for 
Y in the subject, and Y for X in the predi- 
cate, though neither is necessarily, and one at 
least cannot be, a species of the other; which 
is a violation of the next rule. 

Rule VI. Equivalence of Terms to be 
Observed. 

In all substitutions the substituted term must 
be equivalent in signification — i, e., equivalent in 
ratiocinative value — to the term for which it is 
substituted. 

The violation of this rule by the substitution 
of a new term is called the Fallacy of Illicit 
Substitution, 

The rule will cover all cases of legitimate 
substitution of terms whatever ; but it is ob- 
vious, where an ambiguous term is used in a 
different sense from that originally adopted, 
that a new term is in fact illicitly substituted. 
We must add, therefore, as a corollary the 
following: 

Rule VII. The Sense of Terms to Re- 
main Unaltered. 

Every verbal expression^ whether a term or 
proposition, shall, throughout the ratiocination, 
be used in the sense originally given to it. 

The violation of this rule constitutes what is 
called the Fallacy of Equivocation, which is to 



THE RULES OF LOGIC I47 

be regarded as a species of Illicit Substitution ; 
and of this there are two kinds: the first con- 
sisting in shifting the sense of an ambiguous 
term, which is called the Fallacy of Ambiguity ; 
the second, in shifting the meaning of what is 
called an amphibolous sentence, which is a sen- 
tence equivocal by reason of its grammatical 
construction, as, e, g,, the sentence, ** The 
Duke yet lives that Henry shall depose''; 
which may mean either that the Duke shall de- 
pose Henry, or Henry the Duke. If construed 
in the former sense, the subject ofthe proposi- 
tion is, ** The Duke that shall depose Henry " ; 
for which under the latter construction is sub- 
stituted, ** The Duke that shall be deposed 
by Henry/' This is called the Fallacy of 
Amphibology, or, perhaps better, of Amphiboly. 
But these fallacies are of essentially the same 
nature, and will be classed together under the 
one head of Equivocation. 




PART II 
THE DOCTRINE OF FALLACIES 



CHAPTER VIII 

DEFINITION AND CLASSIFICATION OF FAL- 
LACIES 

§ 128. Definition of Fallacies.— A fal- 
lacy may be defined as a false semblance of 
valid ratiocination ; to which it bears the same 
relation as hypocrisy, conscious or unconscious, 
to virtue. Fallacy is therefore a species of 
error, whose specific difference consists in its 
semblance of right reasoning and its conse- 
quent liability to be mistaken for it.* It may 

^ Hobbes, with his usual acuteness, thus clearly explains the 
distinction between error and fallacy : 

*' When we reason with words of general signification {uni- 
versalibus) and fall upon a general conclusion (conclusionem 
universalum) which is false, though it be commonly called 
error, it is indeed an absurdity or senseless speech (pratio 
insignificans)^ — Lev.^ chap. v. According to this view, all 
fallacies are absurdities, i. e., they necessarily involve either a 
contradiction, or the use of non-significant or senseless words. 

149 



150 LOGIC 

consist either in d^ false judgment or 2. false in- 
ference. But, it will be remembered, the terms 
judgment and inference in the logical sense de- 
note, the one intuitive judgment, and the 
other illative inference. Hence, when we 
speak of a false judgment or inference, we do 
not mean a real judgment or inference that is 
untrue (which would involve a contradiction 
of terms), but — as when we speak of a false 
prophet — a pretended or simulated judgment 
or inference that is not really such. 

§ 129. Classification of Fallacies. — 
All fallacies must consist in the violation of 
some one or more of the rules of Logic, and 
hence may be correspondingly classified. Such 
a classification has, indeed, already been sub- 
stantially effected in our statement of the 
logical rules; where, under each rule, the cor- 
responding fallacies have been named. It 
remains, therefore, only to arrange them in 
convenient order, which is done in the table 
that follows: 

Table of Fallacies 

% 130. Fallacies of Judgment. 

I. Illicit Premises. 

(i) Fallacies in Definition. 

Nonsense (or Non-Significance). 
- False Definition. 
(2) Illicit Assumption of Premise {Fetitio 
Principii ). 



CLA SSI PICA riON OF FALL A CIFS I 5 1 

II. Mistaking the Issue, or Irrelevant Conclusion 
{Ignoratio Elenchi), 

* 

§ 131. Fallacies of Inference, or Il- 
licit Substitutions. 

I. Illicit Conversions of Propositions. 
II. Illicit Substitutions of Terms ; Scil. 
(i) 0/ Vocal Signs ^ or Vocables, 
Formal. 
Material. 
(2) Of Notions, /. ^., of Senses of Terms 
{^Equivocation^ Homonymia et Amphi- 
bolia) . 

§ 132. Observations on the Fallacies. 
— Of the tv^o principal kinds of fallacies con- 
tained in the above table, the first — excepting 
the Fallacy of Irrelevant Conclusion — consist in 
the illicit assumption of the propositions to 
be used as the premises of ratiocination. But 
false or nonsensical propositions do not of 
themselves constitute fallacies, but only by 
reason of their use as judgments; for, accord- 
ing to our definition, a fallacy is a false sem- 
blance of ratiocination, and therefore cannot 
exist except as part of ratiocination. Hence 
we are not concerned with the truth or falsity 
or the absurdity of any proposition that may 
be asserted by any one, unless it be used as an 
independent judgment or as the premise of an 



152 LOGIC 

argument, in which case its pretensions may 
be examined, and, if found to be baseless, it 
may be challenged as illicit. 

Where such an assumed premise is either 
non-significant or involves a false definition, it 
is in itself a fallacy, and therefore entitled to 
an independent rank as such. But such fal- 
lacies are innocuous if the sense of the terms 
be preserved unaltered throughout the ratio- 
cination. For all conclusions in which they 
are involved must necessarily be without sig- 
nificance, or, in other words, nonsensical, and 
hence unsusceptible of use. But, as will be 
seen at large as we proceed, the conclusions 
from such premises, being in themselves un- 
susceptible of use, are invariably used as 
equivalent to other and significant proposi- 
tions, and thus inevitably result in the Fallacy 
of Irrelevant Conclusion, or Ignoratio Elenchi, 
which consists in substituting for the conclu- 
sion another proposition {i, e,y the true thesis); 
and which, though for convenience treated 
separately, may itself always be resolved into 
the Fallacy of Illicit Substitution, i, e,y into an 
illicit conversion, or an illicit substitution of a 
term. And the same observation is true gen- 
erally, though not universally, of illicit assump- 
tions of false premises. These, if regarded as 
mere hypotheses, and if no misuse be made of 
the conclusion, are not illegitimate ; but, it will 



CLA SSI PICA TION OF FALL A CIES I 53 

be seen, a conclusion deduced from such pre- 
mises almost invariably either comes in conflict 
with some inconsistent fact, or otherwise fails 
to be sufficient for the purposes the reasoner 
has in view; and thus, almost inevitably, it is 
treated as equivalent to some other proposi- 
tion, thus again presenting a case of Ignoratio 
Elenchi, Hence — if, as we conveniently may, 
we regard all assumed propositions as mere 
hypotheses, and therefore as not illegitimate, 
unless an ill use be made of the conclusion — 
all illicit assumptions of premises must neces- 
sarily result in an Ignoratio Elenchi ; which, as 
we have observed, must necessarily consist 
either in an illicit conversion or the illicit 
substitution of a term. Hence, as all valid 
ratiocination consists in the substitution of 
equivalent (§ 78), so all fallacy must consist in 
the substitution of non-equivalent terms. 

Hence the simplest and most scientific classi- 
fication of fallacies would be to regard them 
all as species of illicit substitution — that is to 
say, as cases, either of illicit conversion of pro- 
positions or illicit substitution of terms; and 
that we have adopted a different mode of classi- 
fication is due simply to the consideration that 
we may thus more conveniently exhibit the 
different sources of fallacy. Hence, as we 
proceed, it will be found that the several fal- 
lacies all have a tendency, as it were, to run 



154 LOGIC 

into each other ; which mainly results from the 
fact that they are all in their essential nature 
the same, differing only in the peculiar sources 
in which they originate; though partly also 
from the fact that, in general, fallacious argu- 
ments are not explicit, and the fallacy may 
vary according to the manner in which we may 
express them. 

In our classification of the fallacies we have 
distinguished as a class the fallacy of '* Mis- 
taking the Issue, or Irrelevant Conclusion,'* 
thus apparently including two separate fal- 
lacies. But this is only apparently so. For 
unless there be some fault in the inference — 
which would constitute another kind of fallacy 
— the conclusion and the premises must neces- 
sarily correspond, and we may therefore regard 
either the illicit assumption or the illicit con- 
clusion as constituting the fallacy. If we re- 
gard the latter as the fallacy, it necessarily 
resolves itself into a case of illicit substitution. 
But, for convenience, we regard it as relating 
to the premises, and thus regarded, it consists 
in the illicit assumption of one proposition in 
place of another — i, e,^ of the actual premise 
for some other proposition more or less resem- 
bling it which is admitted. 

In concluding these introductory observa- 
tions I would refer the student to what is said 
in the conclusion of the Introduction, and 



CLA SSI PICA TION OF FALL A CIES I 5 5 

which, for convenience of reference, is here 
repeated : 

** In our treatment of the subject, the several 
fallacies will be illustrated almost exclusively 
by examples taken from current theories of 
Politics and Morality. Our examples will 
therefore consist, not of mere trivialities, such 
as are so commonly used in works on Logic, 
but of fallacies that, in perverting moral and 
political theory and in corrupting practice, 
have dominated, and still continue to dominate, 
the fortunes of the world. They come to us, 
therefore, as veterans in the army of what 
Hobbes calls the * Kingdom of Darkness,' 
crowned with the laurels of victory '' (§ 13). 

Among these theories there are two fruitful, 
above all others, in examples of logical fallacy 
— namely, the modern doctrine of Absolute 
Sovereignty^ and the Utilitarian Theory of 
Morality ; the former of which may be ex- 
pressed in the proposition that ** Sovereignty 
is, in its essential nature, an absolute power, 
and, as such, unsusceptible either of limitation 
or division''; the latter, in the proposition 
that ** General Utility is the true and only 
standard of justice and injustice, and of right 
and wrong generally.'' Most of our examples 
will be taken from these theories; and these, 
and other current theories used for the same 
purpose, will be found not only to serve as the 



156 



LOGIC 



most effective means of illustrating the nature 
of the several fallacies involved, but also to 
enable us to perceive the frequent use and 
formidable influence of fallacy upon political 
and moral speculation, and to realize how dis- 
astrously and commonly the most vital affairs 
of mankind are thus affected. 




CHAPTER IX 

NON-SIGNIFICANCE, OR NONSENSE — FALLACY 

OF 

§ 133. The nature of this fallacy is explained 
under Rule I. of the Rules of Logic. The fal- 
lacy is of two kinds; namely, (i) where a term 
is used that has an impossible or absurd mean- 
ing or no meaning at all — which constitutes the 
Fallacy of Nonsense in the narrower sense of 
the term ; and (2) where an ambiguous term is 
used without definition — which is called the 
Fallacy of Confusion. But, logically, the two 
kinds are of essentially the same nature, and 
hence are classed together under the general 
head of Non-significance or Nonsense. For 
the purpose of illustrating their nature, they 
will, however, be considered separately. 

I. The Fallacy of Nonsense ^ 

§ 134. In dealing with concrete matters, it 
is difficult to use nonsensical speech without 

^ According to Hobbes (cited supra, § 128, n.), all fal- 
lacies, in their ultimate analysis, may be reduced to this head. 

157 



IS8 LOGIC 

discovering it ; and hence the kind of nonsense 
to which the term is colloquially applied is gen- 
erally of an obvious and transparent character. 
But when we come to deal with abstract terms, 
or terms of second intention, such as are con- 
stantly used in Morality, Politics, and Meta- 
physics, the case is quite different. For here 
not only are we liable constantly to use non- 
sensical or non-significant terms, but it often 
requires the most searching and difficult analy- 
sis to discover that we have done so. Hence, 
the nonsense of which we are to discourse is 
something very different from the nonsense of 
colloquial speech ; which is generally so obvious 
that only foolish people can fall into it, or, at 
least, persist in it. It is a kind of nonsense 
that constantly imposes itself upon the most 
eminent statesmen, jurists and philosophers, 
and even upon the most acute logicians. To 
escape it altogether a man must be endowed 
with more than mortal sagacity, and hence the 
fallacy may be illustrated by examples from 
the writings of the most eminent men. 

Examples 

§ 135. Sovereignty. — The most striking 
example of this fallacy is presented by the 
modern doctrine of Absolute Sovereignty (§ 
132), a doctrine almost universally received by 
modern political writers, and which (with an 



FALLACY OF NON-SIGNIFICANCE I 59 

exception, to be touched upon under the next 
head) has contributed more than any other 
cause to the corruption of political philosophy 
and practice. This will require some explana- 
tion. 

The term Sovereign, in its original and proper 
sense, denoted merely a single ruler or monarch, 
and Sovereignty, the power of this monarch. 
But in modern times the application of these 
terms has been much extended, and the latter 
term is now used in many different ways; of 
which four may be distinguished, namely : (i) 
Personal Sovereignty, or the power of an abso- 
lute monarch — otherwise known as *' the 
Divine Right of Kings'' ; (2) Corporate Sover- 
eignty, or the Sovereignty of the government, 
whether monarchic, aristocratic, democratic, 
or mixed ; (3) Popular Sovereignty, or the Sov- 
ereignty of the state or people; and (4) The 
Sovereignty of Right or the Law^ To which 
may be added as many other senses as abstrac- 
tions can be imagined for the purpose — as, e, g., 
the Sovereignty of Reason, or, in a theocracy, 
the Sovereignty of God. All these different 

^ This expression originated with Aristotle : " Moreover, he 
who bids the law to be supreme, makes God supreme ; but he 
who trusts man with supreme power gives it to a wild beast, 
for such his appetites often make him ; passion, too, influences 
those who are in power, even the very best of men ; for which 
reason the law is intellect free from passion." — Politics, iii., 
xvi. 



l6o LOGIC 

senses of the term are inconsistent with each 
other; and all except the first (now happily ob- 
solete) are — in their direct sense — without 
definite signification, or, in other words, non- 
sensicaL For the government or state, and 
likewise right or law and reason, are purely 
imaginary or fictitious persons, existing only 
in contemplation of mind — i, e,, they are quasi- 
persons only ; and the power of such fictitious 
or imaginary beings must be as imaginary as 
themselves. For the government or state or a 
corporation cannot, properly speaking, be said 
to have rights, or will, or power, or conscience, 
or other human attribute; and when, other- 
wise than as a mere figure of speech, we speak 
of such quasi-^QXsons as having such attributes, 
we talk pure nonsense. And so with reference 
to the sovereignty of God, though the same 
observation is not literally true, yet practically, 
as we can know but little of His will, or the 
exertions of His power, the term, as generally 
used, carries with it no meaning. 

The following examples are in effect identical 
with the above : 

(i) The doctrine of Kant, Rousseau, and 
others, that the will of the government or the 
state is to be regarded as *' the united will of 
the people'' ; which is obviously a mere fiction, 
and, construed literally, not only false, but 
impossible. 



FALLACY OF NON-SLGNIFLCANCE l6l 

(2) The proposition of Hobbes, that the 
effect of the institution of government was to 
create not merely ** a consent or concord " of 
the people, but ** a real unity of them all in one 
and the same person.'' 

(3) The equivalent proposition of Bluntschli 
and others, that the state is an '* organized be- 
ing'' or '' organism y" having a soul and a body, 
a conscience and active powers, and also a will 
different from the wills of the individuals com- 
posing it. 

(4) And finally the celebrated theory of the 
Social Compact or Contract, which served 
Hobbes, Locke, Rousseau, and others as the 
foundation of their respective reasonings; and 
from which, as a premise, their several essen- 
tially different and antagonistic theories are, 
with equal felicity, deduced. 

§ 136. Of Legal Fictions. — These are all 
examples of what lawyers call legal fictions ; 
which are at least as common with the philoso- 
phers as with the lawyers.* In all of them — 
except the last — the government or state is re- 
garded as a body politic or corporation; which 

^ The difference between the lawyers and the philosophers 
in this respect is that by the former the fiction is always recog- 
nized as such, and used merely as a convenient mnemotechnic 
device. It is also used, not as a universal^ but as 2i particular 
proposition — its use being restricted by the maxim, ''''In fic- 
tione juris semper cequitas,^^ But the use of it by philosophers 
is often the reverse. 



l62 LOGIC 

is defined as a fictitious or imaginary person, 
existing only in contemplation of mind, — i,e.y as 
a ^^<3:^/-person, — and the definition is, in fact, 
but a bold metaphor. Hence, as we have said, 
the power of this fictitious or imaginary being is 
as imaginary as itself. For human power can 
exist only in actual human beings; and though 
for convenience we may speak of the power of 
the government as of that of any other corpora- 
tion, yet the expression is always to be under- 
stood as really denoting the concurrent powers 
of certain individuals in the government. 
Hence, when we attribute to the state or gov- 
ernment, or any other corporation or fictitious 
entity, will, conscience, soul, body, sex, or other 
human faculty, feeling, or quality, we speak 
figuratively, and, as in all cases of figurative 
language, if literally, absurdly. The examples 
cited may therefore be more specifically as- 
signed to the class of fallacies called by the old 
logicians the Fallacy of Figure of Speech {Fal- 
lacia Figurce Dictionis), {infra, § 203). 

With regard to the doctrine of a social 
compact, it has not the excuse of being even 
figuratively true. Like the fiction of the Eng- 
lish law that husband and wife are one, it is 
simply an undisguised, recognized absurdity, 
assumed as a first principle. That it should 
ever be asserted would, were it not for experi- 
ence to the contrary, be simply incredible. 



fallacy of non-slgnlficance 163 

§ 137. The Dartmouth College Case. — 
A similar example of this fallacy is presented 
by the decision of Chief Justice Marshall in the 
Dartmouth College case (4 Wheat., 518), where 
it was held that an act of the Legislature re- 
organizing a collegiate corporation was in con- 
flict with the provision of the Constitution of 
the United States forbidding enactment by a 
State of any law ** impairing the obligation of 
contracts. * * It was not perceived that a corpo- 
ration, being a fictitious person, is not capable 
of having any rights, except as representing 
real persons, and that its so-called rights are in 
fact merely the rights of its stockholders or 
other parties interested in it. But in eleemosy- 
nary corporations there are no private parties 
interested, and hence the supposed rights of 
the corporation are in fact those of the State, 
and consequently subject to its disposition. 
For it is absurd to speak of rights that have no 
real owners; and to such rights the Constitu- 
tion—which was designed to protect the rights 
of real persons — can have no application. The 
decision was therefore simply a case of the Fal- 
lacy of Nonsense, of the kind called /^ Figiirce 
Dictionis, 

% 138. Observations on the Fallacy of 
Nonsense. — It may be observed here by the 
reader, who is somewhat familiar with Logical 
Doctrine, that the Fallacy of Nonsense is ap- 



l64 LOGIC 

parently a new kind of fallacy, not to be found 
in the books ; but this is very readily explained. 
For, as we have observed, a conclusion involv- 
ing a nonsensical term, being itself nonsensi- 
cal, can in its proper sense, or rather nonsense, 
be of no use for any purpose, and hence is 
always used as equivalent to some significant 
proposition, and thus becomes an Ignoratio 
Elenchi, Thus the doctrine of Absolute Sov- 
ereignty, like other nonsensical theories, is in 
itself innocuous, and becomes otherwise only 
by illicit use. There can be no harm in saying 
that Leviathan, the creature of our imagina- 
tion, is vested with unlimited power, or even 
to say with Hobbes that he is a ** mortal 
god,** and therefore omnipotent. For his 
power, if left to himself, is no more formidable 
than that of the wooden or brazen gods of the 
heathen. But as in the latter case the power 
of the god is, in practice, the power of the 
priest, so the imaginary power of Leviathan is 
but a word used to cover the actual power of 
some officer or officers of the government; and 
to them the meaning of the doctrine is: *' You 
must not resist us." Hence, invariably, a non- 
sensical term is used only in the argument, and 
the conclusion is always used as equivalent to 
some other and significant proposition, thus 
making a case of Irrelevant Conclusion, or 
Ignoratio Elenchi; under which head it is 



FALLACY OF NON-SLGNLFLCANCE 1 65 

commonly treated. Of this numerous exam- 
ples will be given in the sequel. 

2. The Fallacy of Confusion 

§ 139. This fallacy is recognized in the books 
as one of the most common and pernicious; 
and, indeed, it is a commonplace in philosophy 
that the use of undefined terms is one of the 
most fruitful sources of error. The nature of 
the fallacy is explained under Rule I. of the 
Rules of Logic. A few examples will be suffi- 
cient to illustrate its nature. 

Examples 

% 140. Utilitarianism. — The most serious 
example of this fallacy is presented by the 
theory of Utilitarianism (§ 132 ad fin.)y which 
for the greater part of a century has exercised 
a predominating and pernicious influence over 
English thought. The theory, briefly stated, 
is that general utility is the paramount and 
sole standard of right and wrong and of the 
just and unjust. But the term '* general util- 
ity '' has no definite meaning; because it is im- 
possible to determine from it who are the people 
whose utility or welfare is to be considered — 
whether a mere majority or less, or two thirds, 
or three fourths, or other proportion ; and 



1 66 LOGIC 

hence the proposition must be regarded as non- 
significant or nonsensical. 

§ 141. Education. — So he who asserts the 
benefit of education is, in general, talking non- 
sense. For education is but the development 
of character, — mental, moral, and physical, — 
and may be either good or bad. For there is 
an education of the thief, of the bully, of the 
tramp, as well as of the honest man, of the 
hero, of the efficient man, or of the scholar, 
or statesman, or philosopher. And so, even 
among legitimate kinds of education, there is 
an education of the mechanic, of the farmer, of 
the laborer, of the lawyer, of the doctor, and 
many other kinds. Consequently, when one 
asserts the benefit of education generally, 
without defining the term, the proposition is 
nonsensical. 

§ 142. Protection. — So the man that as- 
serts that he is in favor of the protection of 
American industries is, in general, talking pure 
nonsense. For there are many kinds of pro- 
tection, as, e, g,y (i) The prohibition of all 
foreign imports that compete with our own in- 
dustries; (2) the equalization of the cost of 
production; and (3) the encouragement of in- 
fant industries; and until we are told which of 
these various kinds of protection is intended 
the proposition conveys no definite meaning. 

§ 143. Expansion. — So when an American 



FALLACY OF NON-SIGNIFICANCE 1 67 

announces himself as an advocate of territorial 
expansion he is, generally, talking nonsense; 
for there are many kinds of expansion, among 
which three may be especially distinguished, 
namely: (i) The acquisition of contiguous 
homogeneous territory essential to the safety 
of the government, as, e, g., in the case of the 
purchase of Louisiana; (2) the acquisition of 
contiguous and homogeneous territory desir- 
able as giving room for the expansion of popu- 
lation, but not essential to the safety of the 
government, as, e, g,^ the acquisition of Cali- 
fornia, New Mexico, etc. ; and (3) the acquisi- 
tion of territory far removed from our own, of 
a climate unsuited to our people, and inhabited 
by an alien and non-assimilable race. Such a 
country must be governed by despotic power, 
and its acquisition must therefore be distin- 
guished from other kinds of expansion by the 
name of Imperialism. 




CHAPTER X 

FALLACY OF FALSE DEFINITION 

§ 144. The nature of this fallacy is explained 
under Rule II. of the Rules of Logic. As 
there explained, the fallacy is of two kinds — 
consisting, the one in the use of a term in an 
improper sense, i, e,y in a sense not permitted 
by the usage of the language — the other, in 
using a term in an unreal sense, i, e., as denot- 
ing a notion to which there is no corresponding 
reality. 

The former kind of the fallacy is not admitted 
by logicians generally; for it is an unfortunate 
delusion of philosophers that they are at liberty 
to define a term as they please. But whether 
this claim be admitted or otherwise, it has been 
the source of infinite error; so that the viola- 
tion of the rule, if not regarded as a fallacy, 
must at least be regarded as a most prolific 
mother of fallacy. For where a term is used 
in a novel sense, though clearly defined, it is 
hardly within the power of the human intellect 

i68 



FALLACY OF FALSE DEFINLTLON 1 69 

to emancipate itself from the influence of its 
usual and proper signification. Hence, inevi- 
tably, the use of improper terms will result in 
the fallacy of Ignoratio Elenchi. 

Examples 

§ 145. Whately's Definition of Logic. 
— Whately's definition of Logic as *' the science 
and art of reasoning,'* and of Reasoning as 
consisting solely in syllogistic inference, pre- 
sents an instructive example of the Fallacy of 
False Definition. This definition excludes from 
the province of Logic the doctrine of Judgment, 
and, as involved in this, the doctrine of the 
Term, and also that of the fallacies called Non- 
logical or Material, thus mutilating it of its 
most vital parts. But these subjects are in- 
variably treated of by the logicians, including 
himself, and — as is now generally admitted — 
belong to logical doctrine ; which is an effective 
reductio ad absurdum of the definition. 

§ 146. Stewart's Definition of Reason- 
ing. — From the same false definition of Logic, 
and of reasoning, Dugald Stewart deduces the 
paradoxical conclusion that not only Logic, but 
reasoning itself, is but of little utility; which 
constitutes a still more effective reductio ad 
absurdum of the falseness of the definition.^ 

^ " Of the different elements which enter into the composi- 
tion of reason, in the most enlarged acceptation of the word, 



I/O LOGIC 

§ 147. Locke's Attacks on Logic — 
Locke's diatribes against Logic had their 
source in the same false definition of Logic as 
being merely the doctrine of syllogism. But, 
strangely enough, at the end of his work he 
gives a correct definition of it; which, as we 
have seen, he takes for an invention of his own 
(§110). 

§ 148. Mill's Definition of Logic. — 
According to Mill's definition, ** Logic is not 
the science of belief, but is the science of proof 
or evidence," or, as otherwise expressed, *' the 
science of the operations of the understanding 
which are subservient to the estimation of evi- 
dence." But bearing in mind the essential 
difference between judgments and assumptions 
it will be observed — if we leave out of view 
axioms, which are to be regarded merely as 
laws or conditions, to which the mind operating 
intelligently must conform — that the former 
constitute the first principles of all demonstra- 
tive or apodictic reasoning, and therefore ne- 
cessarily fall within the province of Logic ; but, 
with regard to assumptions^ that Logic is not 
concerned with the evidence of their truth. 
But the term, evidence, in its proper sense, re- 
lates exclusively to assumptions or propositions 

the power of carrying on long processes of reasoning or deduc- 
tion is, in point of importance, one of the least." — Phil, of 
the Mind^ v. ii, p. 154. 



FALLACY OF FALSE DEFINLTLON 171 

in which the significative relations of the term 
are not intuitively perceived; and hence, with 
regard to such propositions, the respective pro- 
vinces of Logic and of the other sciences are 
clearly defined. The latter deal with the evi- 
dence of the propositions assumed ; the former, 
exclusively with inferences from them, upon 
the assumption or hypothesis that they are true. 
Hence the definition of Mill precisely reverses 
the several functions of Logic and of the other 
sciences that furnish it with assumed proposi- 
tions as premises. 

§ 149. Hamilton's Definition of Logic. 
— The definition of Logic as ** the science of 
the laws or forms of thought'' may be cited 
as another example. Logic is concerned, not 
with all thought, but with a particular kind of 
thought only — namely, reasoning; and it is 
concerned, not only with \\\^ forms, but with 
the matter of reasoning. The definition is 
therefore at once too wide and too narrow; it 
would include, e, g,, rhetoric and grammar, 
and would exclude the best part of Logic. 

§ 150. Definition of the Law. — A most 
striking example of the Fallacy of False Defini- 
tion is presented by the definition of the Law, 
invented by Blackstone and adopted as the first 
principle of jurisprudence by Bentham and 
Austin. According to this definition, the law 
is merely an expression of the will of the 



1^2 LOGIC 

government — an obviously false and illegiti- 
mate definition. Yet the theory of Bentham 
and Austin, based on this definition, has abso- 
lutely dominated jurisprudence in England and 
this country for nearly a century; and, as the 
result, English and American jurists and publi- 
cists have lost mental touch with the jurists of 
other countries and ages; and have thus, with 
reference to scientific jurisprudence, been ren- 
dered incapable of dealing with this great and 
important subject. And indeed the effect of 
the theory on the practical administration of 
justice has been scarcely less deleterious. 

§ 151. The Theory of Private Utility. 
— Another conspicuous example of this fallacy 
is furnished by the theory of individual utility 
assumed by Hobbes, Bentham, and Austin as 
the first principle of Morality and Politics; in 
which self-interest is regarded as the sole pos- 
sible motive of human conduct, and right and 
wrong, just and unjust, and good and evil are 
defined as consisting in conformity or noncon- 
formity to that interest. 

§ 152. The Greatest Good of the 
Greatest Number.— Bentham also incon- 
sistently held the theory that '* the greatest 
good of the greatest number*' is the true stand- 
ard of Morality ; which must either be regarded, 
like the theory of General Utility, as simply 
nonsensical, or as holding that the standard of 



FALLACY OF FALSE DEFINLTLON 1 73 

right and wrong and of the just and unjust is 
the good of the majority. An execrable doc- 
trine; for it cannot be asserted that the life or 
faculties or property of an innocent man can 
be converted to the use of another or of others, 
except in the case of a clearly defined right in 
the one and an obligation to submit to it in 
the other. 

§ 153. Maine's Definition of the Law 
OF Nature. — Another example is presented 
by the peculiar and curious view taken by Sir 
Henry Maine of the term Jus Nattirale as 
used by the Roman lawyers, and its equiva- 
lent, the Law of Nature, or Natural Law, as 
used by modern jurists and philosophers. This 
notion, he erroneously assumes, had its origin 
in the supposed state of nature ; which doctrine, 
he says, the Roman jurisconsults borrowed 
from the Greek philosophers. But the term 
Jus Naturaley or Law of Nature, is one of the 
comparatively small class of terms whose mean- 
ing is perfectly definite and settled. As used by 
jurists, it is but another name for Natural Jus- 
tice,* or Right Reason applied to the jural 

* Hobbes's Lev., chap. xxvi. " It is not used among them 
that be learned in the laws of England to reason what thing 
is commanded or prohibited by the law of nature." But, 
"when anything is grounded on the law of nature, they say 
that reason will that such a thing be done ; and if it be pro- 
hibited by the law of nature, they say it is against reason " 
{Doctor and Student, chap. v.). "True law is right reason 



174 



LOGIC 



relations of men ; which, as universally held by 
them, ** is part of the law of every common- 
wealth in the world/* 

conformable to nature " (Cicero, De Rep.). " Right reason is 
what we call law" {id., De Leg.). "Natural law is the 
rule and dictate of right reason " (Taylor, Elements of Civil 
Law). ' ' The law is intellect free from passion " (Arist. , supra, 
§ 135 n.). 




CHAPTER XI 

ILLICIT ASSUMPTION OF PREMISES {PETITIO 
FRINCIPII) 

I. Of the Nature and Several Forms of this 
Fallacy 

§ 154. This fallacy may occur in various ways, 
and it would therefore be an endless task to 
enumerate or classify all its different forms; 
nor would there be any advantage in doing so. 
There are, however, several forms of the fallacy 
that, on account of their frequent occurrence 
and their powerful influence over the minds of 
men, demand a particular consideration, and 
to these our attention will be directed. 

§155 (i). Illicit Generalization. — The 
most important of these, which may be called 
the Fallacy of Illicit Gejteralization, consists in 
the use of a universal proposition in cases where 
the corresponding particular proposition is 
alone admissible. This fallacy is one of the 
most common and formidable, not only in 
popular discourses, but in more pretentious 

12 



176 LOGIC 

works on Politics and Morality ; for almost all 
the wisdom of common sense is embodied in 
this sort of propositions, i. e., particular propo- 
sitions assumed to be universal. Such propo- 
sitions may, indeed, be used with profit by 
men of sense in practical affairs; as, in general, 
when a question presents itself it is easy to 
perceive whether the principle should be ap- 
plied or not; or, if a mistake be made, it is 
corrected by experience; but the masses of 
men are easily misled by them. Hence they 
serve well for rhetorical purposes; for the 
hearer, unless of a critical mind, will in general 
accept them without hesitation. 

Examples 

% 156. Commonplaces.— The most impor- 
tant cases of this fallacy occur in the use of 
Com7nonplaces ; by which is meant, opinions 
current among men generally, or particular 
classes of men, and used as premises for reason- 
ing.^ These are commonly founded upon some 
truth which they purport to express, and to 
which they more or less nearly approximate; 

^ Hence Bacon, as a useful rhetorical device, recommends 
the preparation of tables of Commonplaces, of which he gives 
an example in his De Augmentis ; wherein should be arranged, 
for the use of speakers and writers, in parallel columns, argu- 
ments pro and con^ or theses and anti-theses^ on all questions 
of general interest. 



ILLICIT ASSUMPTION- OF PREMISES 1 77 

SO that there is here, as ** in all things evil, a 
soul of truth.'* But they are hardly ever uni- 
versally true ; and therefore to assume them as 
universals is illicit. 

§ 157. Popular Proverbs. — Of these com- 
monplaces, the most striking examples are 
furnished by popular proverbs; and of these, 
as illustrating precisely the nature of such 
maxims, two may be cited that, in their literal 
expression, are contradictory, but, as maxims 
go, may both be said to be true, i, e,, they are 
each true in certain cases, but neither univer- 
sally. They are the old adages, ** Never put 
off till to-morrow what you can as well do to- 
day *' and ** Never do to-day what you can as 
well put off till to-morrow " ; the first of which 
points out the danger of procrastination, the 
latter, the danger of committing ourselves be- 
fore necessity requires. It may be readily seen 
that, according to circumstances, either of 
these may serve as a useful hint for conduct ; 
but, in using it, the caution of the nautical 
philosopher is to be observed, that '' the bear- 
ing of the observation lies in the application 
of it.'* 

§ 158. Legal Maxims.— Another striking 
illustration of the same class of propositions is 
furnished by what are called the maxims of the 
law; which, in general, are true only 2.% particu- 
lar propositions, i. e,, only in particular cases, 



178 LOGIC 

but are habitually spoken of by legal writers as 
** first principles/' analogous to the maxims of 
science; though every competent lawyer is 
familiar with the fact that they admit of numer- 
ous exceptions. A very large proportion of the 
so-called principles of the law, and of the rules 
founded upon them, are of precisely this nature, 
i, e,y admit of exceptions, and are, therefore, 
true only as particular propositions. And it is 
also a fact that many of these principles and 
rules are opposed by others, equally approved, 
that are contradictory to them. Hence, if we 
regard bulk only, the greater part of the law 
might be readily and advantageously arranged 
in a table of contradictory commonplaces, — /. ^., 
a collection of theses and anti-theses, — as sug- 
gested by Bacon in the De Augmentis; wherein, 
under each topic, one column should represent 
the one side and the other, the other, of the 
various questions that may arise in litigation. 
The cases might also be arranged in the same 
way. 

The above examples are all cases of illicit 
generalization, and will serve to show how wide- 
spread is the use of this particular form of illicit 
assumption of premise. And, it may be added, 
such is the lack of critical acumen in the gener- 
ality of mankind, that the fallacy is seldom 
detected, and consequently it constitutes the 
most powerful of rhetorical devices. 



illicit assumption of premises 1 79 

§ 1 59 (2). Of the Fallacy of Non Ca usa 
PRO Causa, — Another form of the Fallacy of 
Illicit Assumption of Premise is presented by 
the fallacy called ''Non causa pro causa'' ; 
which is also called the fallacy of ** Post hoc 
ergo propter hoc,'' It consists in the illicit as- 
sumption that an event preceding another 
event is the cause of the latter, as, e, g,, that 
a change in the moon is the cause of a change in 
the weather; or that the fact of thirteen dining 
together is the cause of any accident that may 
happen to any one of them ; or that the Dog 
Star is the cause of heat. This is, indeed, one 
of the most familiar of fallacies in political 
arguments, where it is common to argue that 
the condition of the country, whether good or 
bad, is caused by some particular policy, as, 
e, g,y where it is argu,ed alternately, according 
to vicissitudes of events, by the one party that 
a prosperous, by the other that a depressed, 
condition of affairs is caused by the tariff or 
other political measure/ 

^ It will be observed that there are some differences of 
opinion among logicians as to this fallacy. A distinction is 
made between what is called the causa essendi and the causa 
cognoscendi ; or between the cause of an event and the cause 
of our knowing it. These may coincide, as, e. g., when from 
the fact of its raining in the night we infer that the ground 
will be wet in the morning ; where the rain is both the causa 
essendi and the causa cognoscendi. But, when, from finding 
the ground wet in the morning, we infer that it rained during 



l8o LOGIC 

% 160(3). Arguing in a Circle. ^Another 
common form of the Fallacy of Illicit Assump- 
tion is presented by the fallacy called arguing in 
a circle ; which consists in assuming for a prem- 
ise the very proposition to be proved, or one 
obviously equivalent to it, or one that is form- 
ally involved in it.^ When the argument does 
not extend beyond a single syllogism it is 
called a Hysteron Proteron (the First-last).^ 

§ 161 (4). Question-Begging Terms.— 
Another very common and very dangerous 

the night, the causa cognoscendi is the wet ground, from which 
we infer the causa essendi, i. e., the rain. Logic is, however, 
concerned with the causa essendi only so far as it constitutes 
the causa cognoscendi ; and hence logically the distinction may 
be regarded as immaterial. 

^ This occurs most frequently in the use of synonyms, and, 
as observed by V^hately, is peculiarly favored by the composite 
character of our language. It can occur only where the prop- 
osition assumed is so obviously equivalent to the conclusion 
as to be evidently the result of a trick or inadvertence. In 
general the premises assumed are equivalent to, or imply, the 
conclusion ; and the conclusion is arrived at by the substitu- 
tion of an equivalent term ; which is the very essence of ratio- 
cination. Such assumptions are not only admissible, but 
inevitable. Otherwise all syllogisms would be fallacious, — as 
involving z. petitio principii j and inference, inconceivable. 

^ The following is a striking example of this fallacy : 
** Since every unjust act is inexpedient, then no unjust act is 
expedient ; then no expedient act is unjust ; then every expe- 
dient act is just." This has been given as a valid argument. 
But the premise is obviously but an inference from the conclu- 
sion, which is the principle of the reasoning ; and for it the 
thesis has been illicitly substituted as the premise. 



ILLICIT ASSUMPTION OF PREMISES l8l 

form of this fallacy is that of using question- 
begging terms (which is also a case of the Fal- 
lacy of False Definition). It consists either in 
including in the formal definition of a term 
some unproved assumption, as being of the es- 
sence of the conception denoted, or in using 
the term without formal definition, as though 
such assumption were included in its meaning. 
By this method, the propositions from which 
our conclusions are to be deduced, instead of 
being proved as they ought to be, are uncon- 
sciously imbibed by the mind, with the defini- 
tion, or with our conception of the term, and 
the conclusion thus in effect assumed. The 
power of this method of persuasion is well un- 
derstood by many, and unscrupulously used — 
as, for example, by Hobbes and other support- 
ers of governmental absolutism ; who realize 
the truth of Rousseau's observation that ** the 
strongest is not strong enough to continue al- 
ways master, unless he transforms his power 
into a right, and obedience into a duty.'* But 
with the mass of writers the fallacious process, 
though none the less efficacious, is entirely 
unconscious. A notable example of this fallacy 
is usually given by political writers in their 
definitions of ** the State*'; which is simply 
** an independent society of men," but is 
usually defined so as to include in its essence 
absolute power, or some other theory of the 



1 82 LOGIC 

writer. Any recent work on Politics will serve 
to illustrate the fallacy. 

2. Of the Tests of Illicit Assmnption 

% 162. Enumeration of the Tests.— 
There are numerous tests by which the legiti- 
macy of assumed premises may be determined, 
of which the most important and familiar are : 
(i) the '' Instance y'' "^ or ** Extreme Case'*; 
(2) the '' Burden of Proof/' or Onus Probandi ; 
and (3) the Reductio ad Absurdum. These will 
next be considered. 

§ 163. The Instance, or Extreme Case. 
— This test applies most appropriately to the 
Fallacy of Illicit Generalization, and is most 
efficacious in its operation ; though, as is ob- 
served by De Morgan, it is commonly regarded 
as not only inadmissible, but impertinent. It 
consists simply in adducing an exception to the 
proposition assumed. The subject is admi- 
rably treated by the author cited.* 

§ 164. The Onus Probanda— Kn ex- 
tremely effective means of testing the truth of 

^ The term ' ' instance " is commonly used as synonymous with 
** example," but it is said by De Morgan that by the mediaeval 
logicians it was always used to denote an inconsistent example, 
or, in other words, to denote what we would call an instance 
to the contrary, — an expression that would have been regarded 
by them as tautological. 

^ "The application of the extreme case is very often the 
only test by which an ambiguous assumption can be dealt 



ILLICIT ASSUMPTION OF PREMISES 1 83 

a proposition, and of thus exposing an Illicit 
Assumption, is often afforded by considering 
what is the presumption in the case ; or, con- 
trariwise, on which side of the question Hes the 
burden of proof ^ or onus probandi. In general, 
this is on the party affirming the proposition, 
and, in the absence of other presumptions, we 
are always entitled to demand his proofs. This 
simple test will be sufficient to dispose of all 
propositions for which proofs cannot be found, 
but which have been inadvertently assumed ; 
and this test we should always apply to our 
own reasoning, remembering that ** Slowness 
of belief and distrust are the very sinews of 
wisdom." But in certain cases, and especially 
in Moral and Political Science, the test will 
often have a conclusive efficacy. For in 
Morality, Public and Private, or in Jurispru- 
dence or Right, the questions presented are 
generally questions, not of fact, but of right 
and wrong ; and among these there are certain 
fundamental principles, as, e. g,, touching the 
right of personal liberty or security or self- 
ownerships with reference to which the pre- 
sumption is clearly defined, and its cofitradictory 
obviously absurd. Of this kind is the general 
presumption in favor of liberty; which, of 

with ; no wonder that the assumer should dread and protest 
against a process which is as powerful as the sign of the cross 
was once believed to be against evil spirits." — Formal Logic, 



1 84 LOGIC 

itself, is sufficient to dispose of numerous and 
important political theories that, from a neglect 
to consider the onus probandi, have been care- 
lessly or dishonestly assumed. 

§ 165. Of the Reductio ad Absurdum. 
— This consists in reasoning from the conclu- 
sion deduced from the premises assumed to 
some absurd, or admittedly untrue, conclusion ; 
and this method of refutation will apply not 
only to the fallacy of illicit generalization, but 
to all forms of petitio principii whatever. It 
is, indeed, one of the most efficacious means 
that Logic has at its command for the detection 
of fallacy, and will therefore repay an attentive 
consideration. 

Strictly speaking, the phrase would seem to 
indicate that it applies only to the establish- 
ment of the contradictory of the proposition 
under consideration *; but the method has, in 
fact, a much wider application, and the term, 
in common use, a corresponding extension. 
For it is the essential characteristic of all true 

^ In the narrower sense, the term reductio ad absurdum is 
equivalent to the reductio ad impossibile ; of which examples 
are given supra (§ 96, n.). But more generally it is used 
as including all cases where, from the conclusion of an 
argument, the contradictory of some admitted proposition — 
or, in other words, a conclusion contrary to the hypothesis 
— can be deduced. Hence it is called by Aristotle the ' 'Argu- 
ment from Hypothesis." (Hansel's Aldrich^ App., note i, 
p. 228.) 



ILLICIT ASSUMPTION OF PREMISES 18$ 

propositions that they will be consistent with 
each other; and it is an almost equally univer- 
sal characteristic of untrue propositions that 
they will be inconsistent with other proposi- 
tions known to be true. 

This is particularly the case in all the 
different branches of the Science of Human 
Nature ; all of whose parts and particular prin- 
ciples are so connected by numerous relations 
that it is almost impossible to assert an untrue 
principle without coming in conflict with others 
that are self-evident, or readily demonstrable, 
and which have thus come to be universally 
admitted. Hence it may be said that in 
Morality or Politics we may set out from al- 
most any principles, provided we hold them 
with indifference and are capable of abandon- 
ing them when shown to be inconsistent with 
settled principles and known facts. From 
which it may be inferred that the reductio ad 
abszcrdtim in fact constitutes not only an effi- 
cient, but almost an all-sufficient, instrument 
for the detection of fallacy in Moral and Politi- 
cal Science. 

General Examples 

% i66. Locke's Theory of Simple Ideas. 
— A most instructive example of Illicit As- 
sumption of Premise occurs in the fundamental 
assumption of Locke's theory of knowledge; 



1 86 LOGIC 

which IS, that the original notions received in 
the mind from sensible objects are notions of 
the qualities of substances, such as color, hard- 
ness, etc., which he calls simple ideas ; and out 
of which, he holds, all our notions are com- 
pounded. But on reflection it will be perceived 
that the original or primordial notions of the 
mind are the composite notions of substances 
or things ; and what Locke calls '* simple no- 
tions *' are the result of subsequent analysis. 

§ 167. The Obligation of Contracts. — 
It is one of the so-called maxims of the law 
that contracts are obligatory and ought to be 
enforced {Pacta q^icelibet servanda sunt)\ and 
this is commonly assumed as a universal prop- 
osition, as, e. g,, by Bentham and Spencer in 
the examples given below (§§ 180, 181). But 
there are innumerable cases in which it is 
obviously not right that contracts should be 
enforced, and in which, in fact, the law does 
not enforce them ; which is an effectual refuta- 
tion of the principle. The true principle is 
that in case of breach of contract the injured 
party is entitled to compensation — as in the 
case of torts — for the detriment suffered by 
him by the acts of the wrongdoer [i, e,, by the 
making of the contract and its breach). 

§ 168. False Assumption of Fact. — This 
includes innumerable cases, which it would be 
impossible to classify. One of the most in- 



ILLICIT ASSUMPTION OF PREMISES 1 8/ 

teresting is furnished by Tacitus in his account 
of the mutiny of the Pannonian legions on the 
accession of Tiberius, — in the address of the 
soldier, Vibulenus, to the general, Bloesus. 
His brother, he said, coming as a delegate 
from the German army, had been butchered 
by the commands of Bloesus. ** Answer, 
Bloesus,'* he said; ** where hast thou thrown 
away his corpse ? " By which, says Tacitus, 
** he raised such a spirit of frenzy and ven- 
geance that had it not been quickly manifested 
that there was no corpse to be found . 
and that Vibulenus never had any brother, 
they had gone nigh to sacrifice the general.'* 
The example, so far as Vibulenus is concerned, 
was simply a lie, but, in the soldiers, a fallacy 
that would have been readily refuted by apply- 
ing the test of the onus probandu 




CHAPTER XII 

MISTAKING THE ISSUE, AND IRRELEVANT 
CONCLUSION {IGNORATIO ELENCHi) 

% 169. The nature of this fallacy, which is 
explained under Rule IV. of the Rules of 
Logic, is precisely expressed by the first of 
the names we have given it, which is a techni- 
cal term taken from the law. This differs from 
the equally appropriate term Irrelevant Conclu- 
sion only in this, that the former has regard to 
the origin, the latter to the outcome of the fal- 
lacy. Or, in other words, when we regard the 
beginning of the fallacy, we call it Mistaking 
the Issue ; when the end. Irrelevant Conclu- 
sion ; and, in either case, Ignoratio Elencki. 
The two names, i. e.y Mistaking the Issue and 
Irrelevant Conclusion, present, therefore, two 
different aspects of the same fallacy, under 
each of which it will be convenient to consider 
it. 

§ 170. Mistaking the Issue.— This, as is 
well appreciated by the lawyers, is one of the 
most formidable and most common of all fal- 



MISTAKING THE ISSUE 1 89 

lacies. For the most fruitful of all sources of 
fallacy is bias or logical dishonesty, of which the 
expedient of mistaking or misstating the ques- 
tion at issue is one of the most obvious and 
most potent instrumentalities. And as logical 
honesty is, in fact, one of the rarest of intel- 
lectual virtues, it can be readily understood 
that the fallacy must be common. 

§ 171. Fallacy of Several Questions 
OR Issues. — One form of this fallacy may be 
identified with the technical Fallacia plurium 
interrogationum (§ 197), which consists in mix- 
ing in one several questions or issues. As 
defined by Aristotle, it results ** from making 
two questions one, when it escapes notice that 
there are many, and one answer is given, as if 
there was one question only.*' 

The following examples are taken from a 
recent work : 

** ' Did you steal anything when you broke 
into my house last night ? ' * Are you the only 
rogue in your family ? * * Have you quit drink- 
ing ? * * Have you cast your horns ? * (Hence 
sometimes called Cornutus,)'' — (Davis, Theory 
of Thought y 294.) 

The fallacy is readily solved by separating 
the compound question into its several compo- 
nents, — as, ^. ^., in the following: Menedemus, 
Alexino rogante, Numquid^ patrem verberare 
desiisset ? inquitj Nee verberavi^ nee desii ; or, 



IQO LOGIC 

as in the answers of the two thieves to the 
question: ** Did you steal the sheep you have 
in your possession ?**; to which the one an- 
swered, *' He did n't steal the sheep''; the 
other, that '' He did n't have it." 

§ 172. It is added by the author, *' All this 
seems quite frivolous." And another, gener- 
ally accurate, logician says: ** The so-called 
' Fallacia plurium interrogationum ' has not 
been noticed in the text, because it is a rhe- 
torical artifice rather than a logical fallacy." 
(Fowler, Deductive Logic ^ 150.) But it cannot 
be doubted that the fallacy, as described by 
Aristotle, consists simply in mixing several 
questions or issues in one, and therefore comes 
under the head of mistaking the issue; or that 
it is at once a very common and a very for- 
midable fallacy. And especially, it is to be 
observed, it is the hard fortune of the citizen, 
in all ages and countries, that, in general, 
whether by accident or design, no question in 
practical politics is presented to him that does 
not involve this fallacy. 

Thus, in American politics, for some time 
after the war, several questions {^plures inter- 
rogationes) were presented at each federal 
election, namely: (i) as to the expediency of 
the protective policy ; (2) as to that of the re- 
construction policy ; (3) as to that of the con- 
traction of the currency ; and thus practically 



MISTAKING THE ISSUE I9I 

the questions presented to each voter were: 
** Are you in favor of all these policies ? " or 
** Are you against them all ? " So in the last 
election, the issues presented were equally 
numerous — namely : (i) as to the policy of 
protection ; (2) as to the relative advantages of 
the single gold or a bimetallic standard ; and 
(3) — assuming the desirability of bimetallism 
— as to the practicability of adopting it in this 
country alone, without the concurrence of 
other nations. 

In the case put, and in fact in almost all 
political contests, each question involved is dis- 
cussed separately, and the conclusion pro- 
fessedly drawn is simply the affirmative or the 
negative of the particular question, as the case 
may be; but the conclusion intended is, not 
the affirmative or negative of the particular 
question, but that of all of them taken to- 
gether — thus presenting a case of irrelevant 
conclusion. 

Hence, generally, in political contests the 
actual issue presented is simply as to the as- 
cendancy of one of two parties; while the 
voters are persuaded, or persuade themselves, 
that they are deciding some other issue. Hence 
it results — as a general though not as a uni- 
versal proposition — that politics becomes a 
mere struggle for political supremacy. 

§ 173. Irrelevant Conclusion. — All fal- 



192 LOGIC 

lacies of judgment must, as we have observed, 
take the form of irrelevant conclusion (§ 132); 
which, in turn, becomes a fallacy only when 
used as an equivalent to some other proposi- 
tion. Hence the examples of fallacy already 
given, and many of those to be given hereafter, 
will equally serve our present occasion. 

Examples 

§ 174. The Doctrine of Absolute Sov- 
ereignty. — The use made of this doctrine by 
its advocates presents a conspicuous example 
of this fallacy. The doctrine, like all other 
nonsensical theories, is in itself innocuous, and 
becomes otherwise only by illicit use. But it 
is invariably used in some different and signifi- 
cant sense, as, e, g,, Rousseau *s theory of the 
'* Sovereignty of the People,'' which gave rise 
to the various political doctrines rife in the 
French Revolution, and to which historians 
have ascribed the terrible scenes of the Reign 
of Terror ; from which they draw the infer- 
ence that it is dangerous to apply Logic to 
practical politics. But this also is a case of 
Irrelevant Conclusion. For the conclusion 
should be only that Fallacy is dangerous, i, e.y 
not Logic, but the want of Logic. 

§ 175. Sovereignty of the Law.— Of the 
various forms of the doctrine of Sovereignty, 
that of the Sovereignty of Right, or the Law, — 



MISTAKING THE ISSUE 1 93 

as it metaphorically expresses a doctrine at 
once true and fundamentally important, — might 
seem to be unobjectionable were it not that, in 
the direct effect of its language, it is merely 
nonsensical, and therefore liable to be used as 
equivalent to some other form of the doctrine, 
as, e, g,, in the use made of it' by Von Hoist in 
his Constitutional History of the United States ; 
where his expressed conclusion is that ** Sover- 
eignty is One and Indivisible — the Sovereignty 
of the Law,'' ' But his real doctrine — to the 
establishment of which all his arguments are 
marshalled — is that sovereignty is indivisible, 
and therefore vested exclusively, not in the 
law, but in the Federal Government, and not 
to any extent in the States. 

§ 176. Austin's Use of the Doctrine of 
Sovereignty. — An example of this fallacy is 
furnished by Austin and his followers in the 
use made by them of their conclusion, that 

Sovereign power is incapable of legal liinita- 
tion *V which, accepting his definition of the law 
as being merely an expression of the will of the 
sovereign, is quite true, and altogether inno- 
cent; for obviously one's power cannot be said 

^ This — though, if the sense of the term be observed, a 
harmless proposition — is not a very consistent one ; for, as in 
the United States, each State, as well as the Federal Govern- 
ment, has its own independent system of law, it would seem 
to follow that there are several sovereignties. 
13 



194 LOGIC 

to be limited by his own will; but the proposi- 
tion is habitually used in the ordinary sense of 
the terms. 

§ 177. Use of the Doctrine by Hobbes. 
— Another example, precisely similar, is fur- 
nished by Hobbes, who logically deduces from 
his premises the conclusion that '' the right or 
just power '* of the sovereign over the life and 
fortunes of the subject is unlimited ; and the 
corresponding duty of the subject, absolute; 
which, according to his definition of the terms, 
right, justice J and duty, means simply that the 
so-called right of the sovereign is an unbridled 
or lawless poWer, to which prudence demands 
of the subject that he should submit for fear of 
worse consequences. The conclusion, in the 
sense of the terms defined, is, therefore, quite 
true; but it is habitually used by him and by 
modern English jurists as though the terms, 
right J justice, and duty were defined in their 
ordinary and proper sense. 

§ 178. Bentham's Misuse of the Theory 
OF Private Utility. — But the most flagrant 
example of this fallacy is that of Bentham, who, 
having established, or professed to have estab- 
lished, the doctrine oi Private Utility, or Utility 
to the Individual, — which asserts that the sole 
possible motive of human conduct and the 
only standard of right and wrong is self-inter- 
est, — afterwards assumes as equivalent to it the 



MISTAKING THE ISSUE 1 95 

principle of General Utility, and systematically 
uses the latter as the premise established. 

§ 179. Misuse of the Theory of Gen- 
eral Utility. — This theory, in the use 
habitually made of it by Bentham and by 
utilitarians generally, also presents a most in- 
structive example of this fallacy. The theory, 
being non-significant, is in itself innocuous ; but 
it is commonly used as equivalent to the pro- 
position that the interest of the majority is the 
sole test of right, or, as expressed by Bentham, 
** as equivalent to the sacred truth that the 
greatest good of the greatest number is the 
foundation of morals and legislation.'' Thus 
we have the apparently innocuous principle of 
General Utility converted into the execrable 
maxim that the good of the majority is alone 
to be consulted. 

§ 180. Bentham's Defence of Usury. — 
Bentham's celebrated defence of usury has 
been commonly regarded ever since its publica- 
tion as finally settling the question involved; 
but in fact it presents a striking example of the 
fallacy of Ignoratio Elenchi. 

His thesis, as proposed, is to establish ** the 
liberty of making one' s own terms in mo7iey bar- 
gains "; and his conclusion, which is entirely 
legitimate, is that no man, not under disability, 
** ought to be hindered, with a view to his ozvn 
advantage, from making such bargains in the 



196 LOGIC 

way of obtaining money as he sees fit,'' But 
obviously this is to mistake the issue; for the 
question is, not whether one should have the 
liberty of making usurious contracts, but 
whether he should be compelled to perform 
them (§ 167), and hence his conclusion is 
obviously irrelevant. He fails, therefore 
(though the world has thought differently), to 
establish his proposition/ 

§ 181. Spencer's Argument. — Spencer's 
argument — in Social Statics and Justice — for 
liberty of contract is also an example of the 
same fallacy. His first principle is his well- 
known law of equal liberty, namely, *' that 
every man is free to do that which he wills, pro- 
vided that he infringes not the equal freedom of 
any other man,'' From this principle he de- 
duces, with admirable logic, the several per- 
sonal rights that may be summed up in the 
general right of self-ownership, and also the 
right of property, and, as a corollary to the last, 
the right of free exchange, and from that (illog- 
ically, § 189) the right of free contract ; but 
he illicitly assumes, with Bentham, that the 

^ In these observations it will be understood we are con- 
sidering, not the moral or political question as to the propriety 
of enforcing contracts for the payment of interest (on which 
we have nothing to say), but simply the logical question as to 
the validity of an argument in favor of usury that has served 
to convince mankind of its righteousness, and that is univers- 
ally regarded by an unlogical world as conclusive. 



MISTAKING THE ISSUE T97 

question is one touching the liberty of contract, 
and not as to the righteousness of coercing the 
parties (§ 167), which was his thesis. Hence 
his conclusion is essentially distinct from the 
real conclusion intended, which is, that men 
should be compelled to perform contracts. 

§ 182. Berkeley's Theory as to the 
Non-existence of Matter. — This furnishes 
another example. His argument is that, if 
matter exists, it is impossible for us to know 
the fact, or to know anything about it. But 
this conclusion he habitually uses as equivalent 
to the proposition that ** matter, in fact, does 
not exist,'* i, e,, he substitutes the ** non- 
existence of matter'* for ** ignorance of its 
existence." 




CHAPTER XIII 

illicit conversions 

§ 183. Simple Conversion of Universal 
Affirmative Proposition. — The most usual 
form of this fallacy occurs in the simple con- 
version of a universal affirmative proposition, 
as, e, g,y where from the proposition ** Y is 
X " we illicitly infer that ^' X is Y " ; and to 
this form all other cases may be reduced. The 
fallacy is so obvious that it might be supposed 
it could not often occur, but it is in fact very 
common. 

Examples 

§ 184. Confusion of Proposition with 
Judgment. — An example of it seems to be 
presented by the commonly received doctrine 
that ** a proposition is a judgment expressed in 
words ''; which seems to result from an illicit 
conversion of the proposition that a '* judg- 
ment expressed in words is a proposition." 

§ 185. Illicit Conversion by Negation. 

198 



ILLICIT CONVERSIONS 1 99 

— The fallacy frequently occurs in the conver- 
sion of a proposition by negation or contra- 
position. Thus, e, g,^ the proposition ** Y is 
not X " becomes by negation ** Y is not-X " ; 
from which — converting per accidens — we may 
infer that *' Some not-X is Y " ; but not — as is 
often inferred— that '' All not-X is Y." 

By this method any universal afifirmative 
proposition (** Y is X * ') may be converted into 
a proposition between the negatives of its terms 
(/. e,, Not X is not Y); but not, as is often 
done, without converting the terms, — i, e,y 
from the proposition ** Y is X " we may infer 
that '' Not X is not Y," but not that '' Not 
Y is not X" (§91). 

§ 186. An Argument of Hobbes. — A 
striking example of this fallacy is presented by 
Hobbes, that prince of logicians. Justice he 
defines as the keeping of covenants, and injus- 
tice as the failure to keep them. But, accord- 
ing to his theory, covenants become valid only 
upon the institution of government, from which 
they derive their validity. Hence in a state of 
nature there is neither justice nor injustice. 
But he says also: ** Whatever is not unjust is 
just,*' and this conclusion — which is contra- 
dictory to his main position — is obviously 
arrived at by an illicit conversion of the univer- 
sal affirmative proposition, *' Whatever is just 
is not-unjust/' 



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CHAPTER XIV 

ILLICIT SUBSTITUTIONS OF TERMS 

§ 187. Substitutions of terms may consist 
either in the substitution of a new vocable or 
vocal sign, or in the substitution of a new 
sense to the same vocable. The latter is always 
illicit, and constitutes the Fallacy of Equivoca- 
tion, The former will be considered in this, 
the latter in our next chapter. 

The substitution of new terms of equivalent 
signification for terms originally occurring is 
the most common and extensive in application 
of all the processes involved in ratiocination; 
and the corresponding illicit processes — if we 
include equivocation — may be regarded as in- 
cluding all fallacies whatever. Hence the 
examples already given, and especially those 
given under the head of Irrelevant Conclusion, 
will serve equally well to illustrate the fallacy 
now under consideration. 

Examples 

§ 188. Austin's Argument.— Many ex- 
amples of this fallacy are furnished by Austin, 

200 



ILLICIT SUBSTITUTION 20I 

as, e, g.y in substituting for the predicate of the 
proposition that '* The sovereign power is in- 
capable of legal limitation^''' the term ** legally 
despotic,'' and thus inferring from the former 
proposition that government is vested by law 
with despotic power; which is not only untrue, 
but upon his own theory impossible. For, if 
law is but an expression of the will of the 
sovereign, it is equally absurd to say either 
that the sovereign power ** is limited" or that 
** it is conferred'' by law. 

§ 189. Spencer's Argument. — Another 
example is furnished by Spencer in inferring 
from the '' right of free exchange " the ** right 
oi free contract," which is in effect to substitute 
genus for species in the subject of a universal 
affirmative proposition. For excha7ige is only 
a species of contract (v. supra, § 181). It is true 
that the right of free contract cannot be 
doubted, but the substitution is none the less 
a logical fallacy. 

§ 190. Fletcher vs. Peck. — Still another 
example of this fallacy is furnished by Chief- 
Justice Marshall (the greatest and most logical 
of American jurists) in Fletcher vs. Peck, 6 
Cranch, 135; where it was decided that an act 
of the Legislature of Georgia revoking a grant 
of land was in contravention of the provision of 
the Constitution of the United States forbid- 
ding the States to pass any act *' impairing 



202 



LOGIC 



the obligation of contracts^ The argument in 
effect was that a grant is a contract, and that 
this was impaired by the act; which was in 
effect to substitute ** Contract'' for ** Obliga- 
tion of Contract,"' The fallacy is the more 
glaring from the fact that a grant is an exe- 
cMted contract, which carries with it no obliga- 
tion. Hence the constitutional provision must 
be held to refer only to executory or obligatory 
contracts. 




CHAPTER XV 



EQUIVOCATION 



§ 191. The ambiguity of terms and sentences 
{Homonymia et Amphibolia) is undoubtedly the 
most prolific of all sources of fallacy. This is 
recognized by all logicians, and, indeed, by 
philosophers generally; but we doubt that 
many appreciate the extent of the evil or the 
universality of the danger to which men are 
exposed by reason of it, or (especially) their 
own infirmity in this respect. 

** Instances of this fallacy," says Mr. Mill, 
** are to be found in most all the argumentary 
discourses of unprecise thinkers''; a proposi- 
tion true in its literal statement but false in its 
obvious implications; for it implies that the 
proposition is not true of precise thinkers, and 
also (though with becoming modesty) that it is 
not true of the author. But in fact the most 
precise, or, as we would prefer to say, the 
most logical thinkers are liable to fallacy, and 
especially to this kind of fallacy ; and none 

203 



204 LOGIC 

more so than Mr. Mill/ In this respect, if 
fallacies be regarded as intellectual sins, we 
may say: ** There are none righteous. No, 
not one." For it is with logicians as with 
generals: the best that can be said of them is, 
that the greatest are those who commit the 
fewest blunders. Hence the only difference, 
other than degree, between the more precise or 
logical thinker and the unprecise is, that the 
fallacies of the latter are difficult, those of the 
former easy to expose. Hence it may be said 
that, while it is the greatest achievement to be 
right, it is no mean achievement to be clearly 
and unequivocally wrong, i. e,, perspicuous in 
our errors. Hence the value of the political 
theories of Hobbes and Austin, the most logi- 
cal of modern writers; which, though false, 
and even pernicious, are yet full of instruction. 
Nor is the proportion of men of great logical 
genius so large as is generally supposed. They 
are in fact as scarce as great generals, or great 
statesmen, or great poets. Nor is it to be as- 
sumed that philosophical writers are less liable 
to this and other fallacies than the less preten- 
tious classes. ** For it is most true, as Cicero 
saith of them somewhere, that there can be 
nothing so absurd but may be found in the 
books of the Philosophers" (Hobbes, Z^^.,chap. 

^ This is very fully shown by Mr. Jevons {Pure Logic and 
Minor Works, p. 201). 



EQUIVOCATION 20$ 

v.). So, as observed by the author cited, the 
educated classes generally are inferior to the 
vulgar in this respect. For '* those men that 
take their instruction from the authority of 
books, and not from their own meditations, 
[are] as much below the condition of ignorant 
men as men endued with true science are above 
it. For between true science and erroneous 
doctrines, ignorance is in the middle" {Id,, 
chap. iv.). Hence no one should imagine him- 
self free from this general infirmity of mankind ; 
and he who m.ost thoroughly realizes his weak- 
ness in this respect may, like Socrates, be justly 
pronounced the wisest of mankind. All are 
liable to it; and he who supposes he is not is 
simply unaware of his infirmity. 

The nature of the Fallacy of Equivocation is 
obvious, and has been sufficiently explained. 
It remains, therefore, only to illustrate it by 
appropriate examples, and for this purpose the 
examples already given under other heads will 
— with one or two others — be sufficient to serve 
our purposes. 

Examples 

§ 192. Equivocal Use of Nonsensical 
Terms. — Some of the most important cases of 
this fallacy occur from the use of nonsensical 
terms. The very nature of these is that they 



206 LOGIC 

cannot be used for any practical purpose, ex- 
cept by changing their meaning and thus 
giving them a definite sense; and hence, for 
the propositions in which they occur, significant 
propositions are always substituted. . Thus, as 
we have seen, the term Sovereignty varies es- 
sentially in meaning, as used in the several 
doctrines of Personal Sovereignty^ Corporate 
Sovereignty, the Sovereignty of the People or 
State y and the Sovereignty of Right or the Law ; 
all of which different senses of the term are in- 
consistent with each other, and all, except the 
first, in their direct sense, without definite 
signification, or, in other words, nonsensical. 
Yet the term is habitually used by political 
writers without distinguishing the sense in 
which it is used, or without attempting to give 
it any definite signification. But in the prac- 
tical application of the doctrine of Sovereignty 
the term is invariably used as equivalent to 
such definite conclusions as the occasions of 
the writer may require, or as a premise from 
which such conclusions may be deduced; and 
thus the most extravagant doctrines are ap- 
parently established. Of which, as we have 
seen, a striking example is furnished by Prof. 
Von Hoist (§ 175); and others equally ap- 
propriate may be easily collected from almost 
any work touching the subject. 

The same observation will apply to the 



EQUIVOCATION 20/ 

theory of general utility, or Utilitarianism, 
and also to the notions that the will of the 
government is the united will of the people ; 
that the State is an Organism ; that it is 
founded on compact, etc. ; all of which are, in 
their direct sense, in themselves nonsensical^ 
and therefore innocuous, but are habitually 
used as premises to establish all sorts of ex- 
travagant conclusions. 

§ 193. Of Equivocation Generally. — 
The above will suffice for examples of equiv- 
ocations consisting in giving significance to 
nonsensical terms. In illustrating other equiv- 
ocations, the only embarrassment consists in 
the number of examples that crowd upon 
our attention ; but the following may be 
sufficient. 

§194. Argument OF Austin.— One of the 
most striking of these is furnished us by the 
argument of Austin in support of his famous 
position that judicial decisions are in their 
essential nature laws or statutes^ and the judges, 
in fact, legislators ; and another by his equally 
remarkable position that ** Custom does not con- 
stitute part of the law'' ; both of which rest 
upon the equivocal use of the ambiguous term 
** Law ''; which may denote either a laiv or 
statute {lex), or the Law {Jus). 

§ 195. An Argument of Bain. — An ex- 
tremely effective example of this fallacy is also 
14 



208 LOGIC 

furnished by Mr. Bain in his statement of the 
doctrine of Utility. It consists in using the 
term ''party ** in the double sense of a natural 
and of a corporate person. Utility, he says, is 
*' the tendency of actions to promote the happi- 
ness and prevent the misery of the party under 
consideration; which /(^r/j/ is usually the com- 
munity in which one's lot is cast.*' ^ 

§ 196. An Argument Attributed to 
Professor Huxley. — Still another example 
is presented by an argument attributed to Pro- 
fessor Huxley. It consists in the equivocal use 
of the term '' power ^'' which is commonly used 
in two senses, namely, as denoting actual pozver, 
or mighty and as denoting rightful^ ox jural ^ 
power, or right. The argument is as follows: 
** The power of the State may be defined as 
the resultant of all the social forces within a 
definite area. It follows, says Professor Hux- 
ley, with characteristic logical thoroughness , that 
no limit is or can be set to State interference '* 
{A Plea for Liberty, Donisthorpe). 

This fallacy is common to all the Austinian 
school of jurists, and, indeed, constitutes the 
common fundamental infirmity of all their dis- 
quisitions. These jurists, according to their 
theory, have, indeed, no right to use the term 
in any but the former sense; but, as we have 

' Bentham is guilty of the same fallacy {Principles of LegiS' 
lation). 



EQUIVOCATION 



209 



seen, after establishing their conclusions they 
habitually use it as though equivalent to right, 
in the proper sense — a notion that can properly 
have no place in their system. 



CHAPTER XVI 

THE TRADITIONAL DOCTRINE OF FALLACIES 

I 
Aristotle's classification of fallacies 

§ 197. The received classification of fallacies, 
— adopted by the schoolmen from Aristotle, — 
though remarkable for its profound insight, has 
but few pretensions to scientific accuracy; and 
it is to be suspected that much of the obscurity 
and confusion that surround the subject results 
from the undue authority given to it by logi- 
cians. It has, however, so profoundly affected 
logical doctrine and nomenclature that, apart 
from its intrinsic value, it must always remain 
one of the principal subjects for the student's 
attention. 

§ 198. Table of Fallacies. — According 
to this scheme, fallacies are divided into two 
classes, called by the schoolmen and by later 
logicians. Fallacies in Dictione, or in Voce {i, e.y 
in diction or speech), and Fallacies extra Die- 
tioneniy or in Re {i. e., not in diction, but in 

210 



DOCTRINE OF FALLACIES 211 

matter). Of the former class six forms or 
examples are given, and of the latter, seven, 
which are as follows : 

Aristotle s Division of Fallacies 

I. Fallacies in Dictione : 

(i) Hofnonymia (Ambiguity of Terms). 

(2) Amphibolia (Ambiguity of Sentence). 

(3) F. Compositionis (F. of Composition). 

(4) F. Divisionis (F. of Division). 

(5) F. Accentus (F. of Accent). 

(6) F, Figures Dictionis (F. of Figure of 

Speech). 

II. Fallacies extra Dictionem : 

(i) F. Accidentis (F. of Accident). 

(2) F, a Die to Secundum Quid ad Dictum Sim- 

pliciter (Illicit Substitution of Unquali- 
fied for Qualified Terms). 

(3) Ignoratio Elenchi (Irrelevant Conclusion). 

(4) F. Consequentis (Non-Sequitur). 

(5) Petitio Principii (F. of Illicit Premise). 

(6) Non-Causa pro Causa (Mistaking Cause). 

(7) F, Plurium Interrogationum (F. of Several 

Issues in One). 

§ 199. Observations upon this Classi- 
fication. — As will be seen presently, all the 
fallacies In Dictione are simply cases of Equivo- 
cation, and of the fallacies Extra Dictionem all 
except the 4th {F, Consequentis) are Fallacies 
of Judgment ; under which head most of them 
have already been considered at large. The 



212 LOGIC 

excepted fallacy (the F. Consequentis) includes 
all the Fallacies of Inference, ^'kz^'^^. Equivoca- 
tion, It is obvious, therefore, that the current 
expressions {In Dictione and Extra Dictionem) 
— whether from being a mistranslation of Aris- 
totle's language or otherwise — do not truly ex- 
press the nature of the distinction between the 
two kinds of fallacies, and are, therefore, cal- 
culated to mislead us — as they have Whately 
and others — with regard to it. 

§ 200. The true scheme of division is as fol- 
lows: 

Table of Fallacies 

I. Fallacies in Dictione (Equivoca- 
tion). 

(Including the six forms specified in the 
first table.) 

II. Fallacies extra Dictionem, 

( 1 ) Fallacies of judgment. 

(Including all fallacies Extra Dictionem 
given in the table, except F, Conse- 
quentis^ 

(2) F, Consequentis {Non-Sequitur), 

(Including all Fallacies of Inference ex- 
cept Equivocation.) 

(a) Formal Fallacies (/. ^., of Inference). 

(Including Undistributed Middle, Il- 
licit Process.) 

(b) Material Fallacies. 

(Including Illicit Substitutions of New 
Terms.) 



DOCTRINE OF FALLACIES 21 3 

The terms '' FormaV and '' Material Fal- 
lacies'' correspond to the ''Logical'' and 
'* Material Fallacies " of Whately, whose 
'' Semi-logical Fallacies" correspond precisely 
to the fallacies In Dictione of Aristotle, or, in 
other words, to the Fallacy of Equivocation. 
This division of Whately's has, since his time, 
been very generally adopted ; but, as is re- 
marked by Mansel, it ** is not the ancient prin- 
ciple of distinction which is stated with more 
or less clearness by several logicians,'* as, e, g., 
in the following definitions of Sanderson: 

Every fallacy Ft Dictione arises from some 
ambiguity {multiplicitate) of expression." 
*' Fallacies Extra Dictionem are those in which 
the deception happens, not so much from some 
ambiguity latent in the words themselves, as 
from ignoring things " {i, e,, the notions ex- 
pressed). ** The former arise," says Mansel, 
**from defects in the arbitrary signs of thought, 
and hence are generally confined to a single lan- 
guage, and disappear on being translated into 
another. The latter are in the thought itself, 
whether materially, in the false application of 
notions to things, ox formally, in the violation 
of the laws by which the operations of the 
reason should be governed ; and thus adhere 
to the thought in whatever language it may be 
expressed. Under this head are thus included 
both, false judgments and illogical reasonings" 



214 LOGIC 

[i. e,y both Fallacies of Judgment and Fal- 
lacies of Inference) (Mansel's Aldrich^ p. 132). 

II 

FALLACIES IN DICTIONE (eQUIVOCATIOn) 
§ 201 (l) (2). HOMONYMY AND AmPHI- 

BOLY. — These are both cases of the Fallacy of 
Equivocation, the former consisting in the 
illicit use of ambiguous termSy the latter in the 
illicit use of ambiguous sentences. They are 
essentially of the same nature; and we, there- 
fore, as is most in accord with the usage of our 
language, class them together under the com- 
mon name of Equivocations. This fallacy 
has already been fully considered. 

§ 202 (3) (4). Composition and Division. — 
These fallacies are essentially of the same 
nature. They consist in using a term succes- 
sively in a distributive and in a collective sense, 
or, in other words, in substituting for a term 
used distributively the same term used collect- 
ively, or vice versa. The former constitutes the 
Fallacy of Composition, the latter the Fallacy 
of Division. 

The following are examples of the Fallacy 
of Composition: 

3 and 2 {distributively^ are two numbers ; 

5 is 3 and 2 {collectively^ ; 

.'. 5 is two numbers. 

He who necessarily ^^^j- or stays (/. ^., either 



DOCTRINE OF FALLACIES 21$ 

necessarily goes, or necessarily stays) is not a 
free agent ; 

But every one either necessarily ^^^^ or stays 
{i. e,, necessarily does one or the other); 

.'. No one is a free agent. 

The following are examples of the Fallacy of 
Division : 

5 is one number; 

3 and 2 {collectively) are 5 ; 

.*. 3 and 2 {distributively) are one number. 

The angles of a triangle are equal to two 
right angles ; 

A B C is an angle of a triangle ; 

.•. A B C is equal to two right angles. 

All the black and white horses of the de- 
ceased [i, e,, all the black, and all the white 
horses) are the property of the legatee ; 

The piebald horses are black and white 
(/. e,, each is black and white); 

.'. The piebald horses are the property of 
the legatee.* 

Obviously these fallacies (Composition and 
Division) constitute merely a species of equivo- 
cation, i, e,, of Qith^r Hoinonymy or Amphiboly, 

^ The last example is suggested by the celebrated Moot case 
of the legacy of "all the testator's black and white horses." 
The question was, whether the legatee was to have the black 
and the white horses, or the piebald horses, i. e., the horses 
that were each black and white. The legatee claimed that he 
was entitled to both classes ; and, hence, in the one or the 
other of his claims, was guilty of this fallacy. 



2l6 - LOGIC 

% 203 (5). The Fallacy of Accent or 
Prosody {F, Accentus F. Prosodi^),— 
This fallacy is also a species of equivocation, 
i, e,, either Homonymy or Amphiboly. It con- 
sists in varying the meaning of a term or 
proposition by change of accent, tone, or 
punctuation. 

The most extreme case of this is that of 
irony ^ by which the sense is precisely reversed, 
as, e, g.y in the speech of Job to his friends: 
** No doubt but you are the people, and wis- 
dom shall die with you." In this way, /. ^., 
by ironical use afterwards forgotten, the name 
of the subtle doctor, Duns Scotus, has come 
to be the peculiar name of a fool (i. e., dunce). 
The fallacy resulting from changing the sense 
of an ironical expression is too obvious to be 
dangerous, but if it should occur would be a 
case of F, Figtirce Dictionis, 

§ 204 (6). Figure of Speech {F. FiGURyE 
DICTIONIS), — This fallacy (which is also 
merely a species of equivocation) consists in 
the illicit use of figures of speech, or, in other 
words, in substituting for the indirect or fig- 
urative, the direct or literal sense, as in the 
following example: 

** Herod is a fox ; 
A fox is a quadruped ; 
.'. Herod is a quadruped." 



DOCTRINE OF FALLACIES 21/ 

Or as in the following example, which was 
given by a student called on for a syllogism. 
The logical Professor, it may be explained, 
was of corpulent habit, and known as ** Old 
Boll/^ 

" All flesh is grass, the Scriptures say. 
And grass when cut is turned to hay ; 
Now if Death's Scythe Old Boll should take, 
Golly ! What a haystack he would make ! " 

But more serious examples may be found 
among those already given, as, e. g,, the 
equivocal use of the term power in the argu- 
ment attributed to Professor Huxley, and also 
in the misuse of the propositions that "" the 
State is a person,'' that ** it is an organism,'' 
that *' its will is the united will of the people,'* 
that ** it has an interest or welfare distinct 
from that of the people," etc., as heretofore ex- 
plained. A striking example of this fallacy is 
also presented in the famous case of Dart- 
mouth College vs. Woodward (§ 137). The 
fallacy consisted in regarding the college as 
a person; which was only figuratively true. 
For a corporation is a ^^^^^^'^'-person only, i, e,, 
is regarded as a person for certain purposes 
only. 

§ 205. Hamilton strangely speaks of this as 
** a contemptible fallacy," and — as though to 
furnish an example at once of confusion of 



2l8 LOGIC 

things essentially different and of misappre- 
hension of the nature and scope of Logic — he 
couples with the Fallacy of Figure of Speech 
that of Equivocation^ as being, the latter, a 
species of the former, instead of vice versa, as 
is in fact the case. *' These fallacies," he says, 
((' sop his mat a equivocationis, amphibolice, et ac- 
centus) may easily be reduced to sophismata 
figures dictionis ; they are only contemptible 
modifications of this contemptible fallacy." 

But, as is in effect observed by the author to 
whom we are indebted for the above quota- 
tion, when we reflect that nearly all words 
denoting mental or moral qualities or acts — 
which is but to say nearly all terms used in the 
different branches of the science of human 
nature — are in their origin metaphors, derived 
from sensible objects or events as, e, g,, intui- 
tion, perception, apprehension, inference, induc- 
tion, deduction, reflection, education, justice, 
right, wrong, straight, pozver, organic, etc., 
and that these terms still carry with them, to 
a large extent, their material associations, by 
which, as the history of philosophy shows, we 
are continually being misled, we can hardly 
fail to agree ** that the sophism Figurce Dic- 
tionis, so far from being contemptible, is 
worthy of our closest and most watchful 
consideration*' {Theory of Thought, Davis, p. 

27). 



DOCTRINE OF FALLACIES 219 

III 

OF THE FALLACIES EXTRA DICTIONEM 

% 206. Observations. — Of these fallacies, 
all except the fourth are Fallacies of Judgment ; 
and four of them, namely, Ignoratio Elenchiy 
Petitio Principiiy Non Causa pro Causa, and F. 
Phirimn Interrogationmn, have already been 
considered in detail under that head. The 
others, namely, the Fallacies of Accident, of 
Secundum Quid, and of the Consequent — of 
which the first two are also Fallacies of Judg- 
ment — remain to be considered. 

Logicians are widely at variance with refer- 
ence to the nature of these fallacies; and, if 
we may judge from the translations and from 
the confusion reigning over the subject, Aris- 
totle's own explanation of them must be re- 
garded, in some particulars, as hopelessly 
obscure. Hence, though I have attempted to 
interpret his meaning correctly, I am by no 
means sure that I have succeeded in this better 
than others. It may, however, be claimed for 
the exposition of the subject here given that it 
is at least intelligible and consistent, and that, 
in connection with the rest of Aristotle's 
scheme, it renders his classification of the fal- 
lacies complete. And, it may be added, it is 
in accord with the best authorities. 



220 - LOGIC 

§ 207. The Fallacy of Accident {F, Ac- 
CIDENTIS). — This fallacy has its source in the 
assumption that an accident of some of the 
significates of a term, or of all its significates 
for a certain time, is an accident of the term, 
and therefore predicable of it without qualifi- 
cation {i.K supra, § 49.) This assumption in 
the case of an inseparable accident of all the 
significates of the term is, indeed, legitimate; 
for obviously such an accident may always be 
predicated of all the significates of the term, 
and hence of the term. But with separable ac- 
cidents of the significates of a term, it is other- 
wise; for, though these are commonly spoken 
of as accidents of the term, they are not such 
in fact, for their relation to the term is tem- 
porary or transient/ Hence such an accident 
can be predicated of the term only for so long 
as it continues to be an accident of it, or, in 
other words, only with relation to some par- 
ticular time expressed or understood. For in 
the logical proposition the copula has no rela- 
tion to time, but expresses simply a permanent 
significative relation between the terms, and 

^ The terms separable and inseparable accidents can apply 
only to real individuals, and hence only to concrete terms or 
terms of first intention. W^ith relation to these the distinc- 
tion is sufficiently obvious. Thus, e. g,, with reference to 
Socrates, " Stagyrite" is an inseparable accident ; " standing," 
** sleeping," etc., separable — the last being predicable of him 
only at times. 



DOCTRINE OF FALLACIES 221 

hence a separable accident cannot be predi- 
cated generally of a term. For, as is said by 
Aristotle, *' it is uncertain when [/. ^., at what 
times] an assertion can be made of a thing 
present from accident*'; or, in other words, 
whether at any given time the accident con- 
tinues to exist {Soph, Elench, chap. xxiv.). 
Thus, e, g,y an attacking party might be rightly 
informed at a given time that the enemy was 
sleeping, and hence conclude that it would be 
safe to attack him ; but it might be a fatal 
error to assume the truth of the premise as 
continuing to exist an hour later. 

§ 208. Definition of the Fallacy. — The 
fallacy may therefore be defined as consisting 
in predicating of a term a separable accident of 
its significates without qualifying it by refer- 
ring to the time at or during which it is inher- 
ent ; or, in other words, in assuming, in place of 
a proposition of which the predicate is an ac- 
cident thus qualified, another proposition of 
which the predicate is the accident unqualified ; 
as if, e, g,y from knowing a man is lame we 
should assume that he is permanently lame. 
Or the subject may be more generally illus- 
trated as follows: Let Y denote the subject 
(** John '*), A the ^(:<;^^^;^/<^/ predicate (** tem- 
porarily lame," i, e., 'Mamefor the time being"), 
and X the general predicate (^' permaiiently 
lame '*); then we may be entitled to say *' Y 



222 LOGIC 

is A*'; but to assume, in place of this, that 
Y is X would be to substitute for A the term 
X, i, e,, species iov genus in the predicate of a 
universal afifirmative proposition. For the 
class of '* temporarily lame'' will include all 
the ''permanently lame,'' and many others. 

It will be noted here that there is necessarily 
a significative relation between the accidental 
and the general predicate, namely, that of 
partial coincidence. Hence, to substitute X 
for A is, in effect, to substitute AX (/. ^., 
** Some A "^ for A, which presents a case of 
illicit substitution of species for genus in the 
predicate of an affirmative proposition. 

It will also be observed that the Fallacy of 
Accident is defined as consisting in the illicit 
assumption of a premise. But, where the same 
fallacy occurs in a formal inference, it con- 
stitutes the Fallacy of Undistributed Middle, 
which is a case of Non-sequitur or F, Consequen- 
tisy as may be thus illustrated : 



Some A is X 

Yis A 

.\ Y is X 



The stock example of this fallacy, which I 
have taken from Aldrich, is as follows: 

** What you have bought you have eaten; 
you have bought raw meat; therefore you 




DOCTRINE OF FALLACIES 223 

have eaten raw meat " {Quod emisti cojnedisti ; 
crudum emisti ; ergo crudum comedisti); which 
may be expressed in the following syllogism, 
which, in form, is unobjectionable: 

The meat you buy is raw ; 
The meat you eat is the meat you buy ; 
.*. The meat you eat is raw. 

The fallacy here may be regarded as a case 
of equivocation, consisting in the use of the 
term ** raw '* in the major premise in the sense 
of '* raw zvhen bought^'" and in the conclusion 
in the sense of *' raw when eaten,'' But if the 
term ''raw'' be construed simply in both 
cases (/. ^., as used without qualification), the 
fallacy must be regarded as a case of F, Acci- 
dentisy consisting in the illicit assumption of 
the major premise. For all that can be right- 
fully affirmed is that the meat bought is raw at 
the time of purchase; instead of which it is 
assumed that it is permanently raw. For, 
as we have observed, in the logical prop- 
osition the copula includes both the future 
and the past, and the significative relation be- 
tween the terms is asserted, not as true only 
at the moment of assertion, but before and 
afterwards; and hence a universal proposition 
may always be negatived by showing an in- 
stance to the contrary y either in the past or in 
the future. 



224 LOGIC 

The following examples are furnished us by 
Aristotle, and are given as paraphrased in the 
notes of Mr. Owen's translation: 

** Do you know what I am about to ask ? 
No. But I am about to ask whether virtue is 
good. Therefore, you know not whether virtue 
is good.*' 

** Do you know who approaches ? No. 
But Socrates approaches. Therefore, you do 
not know Socrates.'' 

Here in each case the most obvious source 
of the fallacy is in the use of the equivocal 
terms, ** What I am about to ask " (in the 
first case), and ** Who approaches " (in the 
second). But this ambiguity may be removed 
and the arguments expressed syllogistically in 
unobjectionable form as follows: 

( 1 ) The question, I a7?i about to ask, is unknown to 

you. 
The question whether virtue is good is the question 
I am about to ask, 
.'. The question whether virtue is good is unknown 
to you, 

(2) The man approaching is unknown to you, 
Coriscus is the man approaching, 

.*. Coriscus is unknown to you. 

Indeed, even as thus expressed, the most 
obvious solution of both these fallacies is still 
to regard them as cases of equivocation, con- 



DOCTRINE OF FALLACIES 22? 

sisting in using the term '' unknown to you '* in 
a double sense, t. e.^ in the major premise in 
the sense of ** unknown to you before you are 
told,'' and in the conclusion in the sense of 
** unknown to you after you are told^ But if 
the term be regarded as used in the same sense 
in both places, the case is evidently one of F, 
AccidentiSy consisting in the illicit assumption 
of the major premise, or, in other words, in 
the illicit substitution of the unqualified term, 
** unknown to you,'' for the qualified term, 
** unknown to you before you are told," which 
alone was admissible as a predicate. 

§ 209. The Fallacy of Secundum Quid 
{f. a die to secundum quid ad dictum 
SIMPLICITER), — This fallacy consists in as- 
suming an unqualified in place of a qualified 
proposition. But as the copula has but one 
meaning, a proposition can be qualified in no 
other way than by qualifying one or both of 
its terms. Hence the fallacy must consist in 
substituting for an unqualified a qualified term. 

But a term can be qualified {i, e,, its signifi- 
cation or extension altered) only by coupling 
with it another term that partly, but not 
wholly, includes it, thus making a new term of 
less extension, as, e, g,, men by white, which 
gives us for the new term, white men; or, 
more generally, Z, Y, or X, by A, which 

gives us, for new terms, AZ, AY, and AX, all 

15 



226 LOGIC 

included in, but of less extension, than the 
originals ; or, in other words, the class denoted 
by a qualified term will always be a species 
of the class denoted by the unqualified term. 
Hence the Fallacy of Secundum Quid is simply 
a particular case of the illicit substitution of 
genus for species in the subject of an affirmative ^ 
or in either the subject ox predicate of a negative 
proposition. 

Where the illicit substitution occurs in the 
inference, the fallacy belongs to the general 
class of fallacies that go by the name of F, 
Consequentis or Non-sequitur ; but if in one 
of the premises, it constitutes the Fallacy of 
Secundum Quid, now under consideration; 
which must, therefore, like the F, Accidentis, 
be regarded as a case of Illicit Assumption of 
Premise, or of Petitio Principii, The Fallacy 
of Secundum Quid may therefore be defined as 
consisting in the illicit assumption of a premise 
in which there is an unqualified term in place 
of another in which the same term is qualified ; 
or, as expressed by Aristotle, is assuming that 
** what is predicated in part is spoken simply '* 
{Soph. Blench, y chap, v., 2). 

§ 210. Of the Relation between the 
Fallacies of Accident and Secundum 
Quid. — The Fallacy of Secundum Quid will 
therefore include the Fallacy of Accident, which 
is but a particular case of it. Or, in other 



DOCTRINE OF FALLACIES 22/ 

words, the latter is a species of the former, its 
specific difference being that the qualification 
omitted relates exclusively to time ; whereas, 
in the case of Secundum Quid generally, the 
omitted qualification may relate either to time 
or to place, quantity, or any other quality or 
attribute. 

The following examples of the F, Secundum 
Quiddity taken from various sources: 

(i) Pernicious things are things to be forbidden; 
The use of wine is pernicious ; 
Therefore the use of wine is a thing to be for- 
bidden. 

(2) Things productive of bad effects are unfit for 

use ; 
Antimony is a thing productive of bad effects ; 
.'. Antimony is unfit for use. 

(3) Things productive of bad effects are to be dis- 

couraged ; 
Eloquence is a thing that produces bad effects ; 
.*. Eloquence is to be discouraged. 

(4) Things destructive to human life are to be 

avoided ; 
Medicine is a thing destructive to human life ; 
.*. Medicine is to be avoided. 

(5) Y is X 
Zis Y 

.-. Z is X. 



228 LOGIC 

In each of these arguments — all of which are 
regular in form — the fallacy consists in the 
illicit assumption of the minor premise, consist- 
ing in substituting in the subject an unqualified 
in the place of a qualified term, viz., in the 
first, the term '' use'' for '' excessive use''; in 
the second, ** antimony " for ** antimony when 
misapplied" ; in the third, ''eloquence" for ''elo- 
quence when abused" ; in the fourth, " medi- 
cine" for ** medicine when used by ignorant 
doctors" ; and in the fifth, — denoting by A any 
term qualifying Z, — Z, for AZ. The fallacy, 
therefore, in each case consists in the substitu- 
tion of genus for species in the subject of an 
affirmative proposition, and hence differs from 
the corresponding fallacy of inference simply 
in being an illicit assumption instead of a 
formal inference. 

§211. Erroneous Views of Logicians 
AS TO THESE FALLACIES. — The F. Accidentis 
was defined by Aldrich, and probably by the 
old logicians generally, as in the text. But 
Whately, who is followed by most of the later 
logicians, defines it as the converse of the 
Fallacy of Secundum Quid ; and since then the 
subject has been involved in the greatest con- 
fusion. The prevailing view is thus expressed 
by De Morgan : 

" (i) The Fallacia Accidentis and (2) that 
a dicto secundum quid ad dictum si^npliciter. 



DOCTRINE OF FALLACIES 229 

The first of these ought to be called that of 
a dicto simpliciter ad dictum secundum quid, for 
the two are correlative in the manner described 
in the two phrases. The first consist in infer- 
ring of the subject with an accident that which 
was premised of the subject only, the second in 
inferring of the subject only that which was 
premised of the subject with an accident " {For- 
ma I Logic, p. 250). 

The latter process is undoubtedly fallacious, 
but the former — i, e,y inferring of the subject 
with an accident that which was premised of 
the subject only ; or, in other words, of infer- 
ring that what is predicated of a ter^n generally 
may be predicated of the term as qualified by 
an accident — is entirely legitimate. For to 
qualify a term, either by an accident or other- 
wise, is simply to diminish its extension, and 
thus to create a subclass or species of the class 
denoted by the unqualified term; and accord- 
ing to the dictum, whatever may be predicated 
of the unqualified term or genus may be predi- 
cated of the qualified term or species; or, in 
other words, in any universal proposition of 
which the unqualified term is the subject, the 
same term qualified by an accident may be legiti- 
mately substituted for it; that is to say, sym- 
bolically, denoting by AY, Y as thus qualified, 
if Y is X, then AY is also X; as may be thus 
illustrated : 



230 LOGIC 




In illustration of the supposed fallacy {F. a 
dicta simpliciter ad dictum secundum quid) De 
Morgan and others give us the story of the 
stork, from Boccaccio, which, as quoted by 
Professor Davis, is as follows : 

** A servant who was roasting a stork for his 
master was prevailed upon by his sweetheart 
to cut off a leg for her to eat. When the bird 
came upon the table the master desired to 
know what was become of the other leg. The 
man answered that * the stork never had but 
one leg.' The master, very angry, but deter- 
mined to strike his servant dumb before he 
punished him, took him the next day into the 
fields, where they saw storks standing each on 
one leg, as storks do. The servant turned 
triumphantly to his master, upon which the lat- 
ter shouted, and the birds put down their other 
leg and flew away. * Ah, sir,* said the servant, 
* but you did not shout to the stork at dinner 
yesterday ; if you had done so, he would have 
showed his other leg too.' " 

The gist of which, the author says, ** is the 
assumption that what can be predicated of 
storks in general can be predicated of roasted 



DOCTRINE OF FALLACIES 23 1 

storks, — a dicto simpliciter ad dictum secundum 
quid,'' But undoubtedly (assuming for the 
sake of the argument that dead and roasted 
one-legged storks belong to the genus stork) 
whatever may be universally predicated of 
storks may, unless the dictum be a delusion, be 
predicated of roasted and one-legged storks as 
well as of others. The error, therefore, con- 
sists, not in an incorrect inference of the 
particular proposition from the universal prop- 
osition including it, but in the illicit assump- 
tion of the universal proposition that whenever 
you shout at a stork it will put down a second 
leg, though it may have only one leg, and be 
dead and roasted. 

§ 212. F, Consequentis, — There is much dis- 
pute as to the nature of the fallacy intended by 
Aristotle under this name. De Morgan and 
other logicians — following Aldrich — regard it 
as consisting in the ** afifirmation of a conclu- 
sion '' which does not follow from the premises, 
or, in other words, as but another name for a 
Non-scquituTy which is at least the most con- 
venient view. 

§ 213. Classification of Fallacies of 
THIS Kind. — According to this view, the F. 
Consequentis will include (i) the v^^x^Xy formal 
fallacies, commonly known as fallacies of the 
syllogism ; and (2) all the material fallacies of 
inference except Equivocation. The former 



232 



LOGIC 



have been sufficiently treated in considering 
the rules of the syllogism ; the latter, under 
the head of Substitution. The former as well 
as the latter, and also the fallacies of Equivoca- 
tion (or In Dictione), are also, it will be remem- 
bered, fallacies of Substitution. 




APPENDIX OF NOTES 

A-§4 

Perhaps, when men understand that the main 
sources of Philosophy are to be found in the 
study of words, we may hope to escape the dreary 
treadmill on which philosophers have hitherto been 
exercising themselves. All progress in Philosophy 
that has been made has been the result of the un- 
conscious observation of this method — as, e, g.^ the 
work of Locke, which, though weak in its meta- 
physics, constitutes the greatest contribution to 
philosophy made in modern times; and which, as 
shown by Home Tooke, is merely an essay on lan- 
guage. ** Perhaps," he says, " it was for mankind 
a lucky mistake (for mistake it was) which Mr. 
Locke made when he called his book an Essay o?t 
the Human Understanding, For some part of the 
inestimable benefit of that book has, merely on ac- 
count of its title, reached to many thousands more 
than, I fear, it would have done had he called it 
**A Grammatical Essay," or ** A Treatise on 
Words or Language " {^Diversions of Pur ley), 

B— § 6 

Comparing the physical sciences and the mathe- 

233 



234 LOGIC 

matics with the moral sciences, the latter are infi- 
nitely the more difficult of achievement; and also 
infinitely more important to the welfare of man- 
kind. For under the name of the moral sciences 
are included all the several branches of the 
Science of Human Nature; which is obviously the 
principal concern of mankind, and as such the sci- 
ence to which all others are to be regarded as sub- 
sidiary. This was the distinguishing characteristic 
of Socrates* philosophy. It was expressed in the 
injunction written over the portals of the Delphic 
god: '* Know thyself! " and in modern times has 
been finely rendered: ** The proper study of man- 
kind is man." It is also embodied in the fine old 
term, the Humanities^ which signifies those parts of 
education that have for their end the development 
of our manhood or humanity, and which must 
therefore constitute the essential elements of a 
rational general education. 



8 



This was the great discovery of Socrates; to the 
preaching of which, as the gospel most needed by 
men, his life was devoted. Nor have there been 
wanting, in succeeding ages, philosophers — and 
those the greatest — to continue his mission. But so 
averse are men to being convinced of their errors 
that nothing is more odious to them than the at- 
tempt. Hence, generally, all means of defence are 
regarded as legitimate, — that is to say, not only fal- 
lacies, but falsehoods and slanders, and, at times, 



APPENDIX OF NOTES 235 

the prison, or the rack, or death. Thus Socrates 
was poisoned for this offence only; which, though 
otherwise atrocious, was creditable to the Athen- 
ians, as at least proving an uncomfortable mental 
susceptibility to the power of reasoning or Logic. 
For in modern times we have invented a better 
method of dealing with such fellows, and have 
developed a mental integument as impervious to 
the weapons of reason as that of the elephant or 
rhinoceros to the weapons of the primitive hunter; 
and against which the Socratic wit would batter 
m vain. Thus we are enabled to dispose of those 
who would disturb our mental peace and compla- 
cency, by simply refusing to listen to them, and by 
extolling our own idols, — like the Ephesians; who, 
in answer to the preaching of the apostles, *'all 
with one voice, about the space of two hours, cried 
out: Great is Diana of the Ephesians." By these 
two means — w^hich have been aptly called ''the 
conspiracy of silence," and *' the society of 
mutual admiration " — our opinions are now im- 
pregnably buttressed. Thus we live in a sort of 
Fools' Paradise ; though, as Bacon says, ** the 
apotheosis of error is the greatest evil of all, and 
when folly is worshipped, it is, as it were, a plague- 
spot upon the understanding " {^Nov. Org.^ bk. i., 
aph. Ixv.). 

D— § II 

The disuse of Logic must necessarily affect the 
teaching of Moral and Political Science, Metaphys- 
ics, and the Science of Human Nature generally; 



236 LOGIC 

for the investigation of which it is indispensable. 
Hence, as the proper study of mankind is man, it 
may be said that the universities of the day have 
fallen behind their predecessors in efficient perform- 
ance of their most essential function. It should 
not be forgotten that the task of reorganizing Euro- 
pean society as it emerged from the chaos of the 
dark ages was mainly effected by such men as 
Lanfranco, Suger, Anselm, and other churchmen — 
graduates of the mediaeval schools and universi- 
ties, and consequently educated in Logic and Law; 
studies the art of teaching which has been lost by 
our modern universities, and which yet surpass all 
others as means of a rational education. That this 
is the case with Logic, it is the aim of this work to 
show; with regard to the Law, the opinion of Burke, 
by those competent to judge, has been generally 
accepted, — that it '' is one of the first and noblest 
of human sciences — a science which does more to 
quicken and invigorate the understanding than all 
other kinds of learning put together.** Though, 
he adds, *' it is not apt, except in persons happily 
born, to open and liberalize the mind exactly in 
the same proportion." 

E-§ 12 

The peculiar merit of Logic, as one of the Hu- 
manities, is its perfect cognoscibility, and the 
consequent facility with which it can be taught. 
Arnauld in the preface to the Port Royal Logic 
tells us that he undertook to teach a young noble- 



APPENDIX OF NOTES 237 

man all that was useful in Logic in four days, and 
successfully performed the task. The claim is 
seemingly extravagant, but as his notion of Logic 
was confined mainly to the doctrine of the syllo- 
gism, and to so much only of the doctrines of the 
term and of the proposition as was incidentally 
necessary, and as the student was a young gentle- 
man of remarkable ability, it may very well be 
credited. Nor will a more complete and compre- 
hensive study of the subject add much to the labor 
of mastering it ; if indeed it will not facilitate the 
task. The general diffusion of logical culture can-, 
not be regarded, therefore, as a vain aspiration. 
The subject requires no preliminary culture other 
than the studies usually taught in the common 
schools, and may be readily mastered by almost 
any young man of average ability and the proper 
age — say sixteen or seventeen. x\nd this will espe- 
cially be the case with one who has thoroughly 
mastered the elements of algebra and geometry. 
Thus it is quite possible to devise a very brief 
course of study sufficiently thorough to train the 
student as a reasoning creature, and to make him 
equally competent with the graduates of our great 
universities to grapple with all the great problems 
of Politics and Morality; and, indeed, until our 
modern university education be reformed, even 
more so. This was illustrated by the mediaeval 
universities, to whose graduates, as we have ob- 
served, the reorganization of society at the close of 
the dark ages was entrusted, and by whom the 
task was successfully accomplished; nor do I think 



238 LOGIC 

it extravagant to say that alongside of them in prac- 
tical politics our modern graduates would be but 
children. Of the subjects taught outside of The- 
ology the principal, as we have said, were Logic and 
Law, and these must be regarded as the most essen- 
tial parts of a rational education. The latter will 
require long and persevering study, but a thorough 
logical training will render the student competent 
to master it; and without such training — either 
systematically taught to him at the outset, or grad- 
ually acquired in the study of the law itself — its 
mastery is impracticable; and the same observation 
is true with reference to Political Science generally. 

F-§ 13 

I have been admonished by a friend that the use 
of examples of this kind in an elementary work 
may be hazardous; and this, I understand, on the 
double ground that the younger student may find 
it difficult to understand them and the older, regard 
them as disputable; and that thus they must prove 
to the one a stumbling-block, and to the other fool- 
ishness. With regard to the last objection, it is to 
be admitted that if any of the examples are in fact 
disputable, the objection is well taken. But I am 
persuaded that, if they appear so to any one, it is 
only because of the universal bias of men in these 
unlogical times in favor of their opinions, and that 
any one who will provisionally reject all prejudice 
will see at once that the argument is in every case 
demonstrative. Or if in any case I am deceived, 



APPENDIX OF NOTES 239 

then my own reasoning will serve for example. 
With regard to the younger student, the opinion 
seems to be that it would be better to illustrate 
the nature of the fallacies by the more familiar 
examples of the character commonly used in the 
current logics. But this, I think, to be a great 
mistake. The fallacies are themselves sufficiently 
simple to be readily understood, and trivial 
examples merely serve to lead the student to 
suppose that he is in no danger of falling into 
them. I have therefore thought it far better to 
take my examples from theories that have played 
and are now playing a great part on the stage of 
history. Nor are these, when treated logically, at 
all difficult, with a little reflection, to understand; 
and indeed it is to be assumed that, if a young man 
has arrived at the age at which he can study Logic 
profitably without some familiarity with these ques- 
tions, his education has been much neglected. 
Neither this nor any part of my work can, indeed, 
be understood without the independent thought of 
the reader; but this also I consider not only a great 
advantage, but an essential condition to the right 
exposition of the subject. For though the princi- 
ples of Logic are extremely definite, and therefore 
readily cognoscible, yet, as already observed, they 
require for their mastery the same kind and degree 
of study as is required by the mathematics; and 
there is no royal road to Logic any more than to 
geometry. If the student, therefore, will take the 
trouble to work out thoroughly these examples, and 
others of the same character (of which many will 



240 LOGIC 

suggest themselves), he will achieve not only a 
mastery of the principles involved in them, and of 
the practical use of Logic, that cannot be otherwise 
attained, but also an accurate, though limited, 
knowledge of all the great political, social, and 
moral questions involving the welfare of mankind; 
which, better than anything else, will serve as 
an introduction to those studies. I have also, 
in the use of these examples, another point in 
view, which is, that, by means of the application 
of logical principles, these apparently difficult 
problems are readily solved, and the most im- 
portant heresies in Politics and Morality that 
afflict mankind exposed; and thus are proved, by 
practical illustration, the theses with which I com- 
menced, — that in all the moral sciences the use of 
Logic is essential, and that the confused and un- 
satisfactory condition of the literature of these 
subjects is due to the decay of Logic. 

In conclusion, however, I would say that while 
regarding the current examples used in the logics 
as inadequate for the illustration of the subject, I 
have not neglected them, but, in the chapter on 
the Traditional Doctrine of Fallacies, have con- 
fined myself mainly to them. 

G — § 14 

This is strenuously objected to by Hamilton. 
*' Dr. Whately," he says, ** is contradictory. . . ., 
In some places he makes the operation of reasoning 
not only the principal, but the adequate object of 



APPENDIX OF NOTES 24 1 

Logic. ... In others, he makes this total or 
adequate object to be the language. But as there 
cannot be two adequate objects, and as language 
and the operation of reasoning are not the same, 
there is therefore a contradiction " {Logic^ 11). 

But though language and reasoning are not the 
same, yet they are the same so far forth as Logic 
is concerned with either; for, as Logic has to deal 
only with reasoning expressed in language, it is 
necessarily concerned with both to the same extent; 
and we may say, with equal propriety, that the 
subject-matter of Logic is either language or 
reasoning. 

The error of Hamilton lies in the illicit assump- 
tion that the term ** language " is equivalent to the 
external logos, /. ^., the expression, as opposed to 
the inward thought. But if language be construed 
as denoting both the thought and the expression, as 
it should be, the only objection disappears; and 
when thus construed, the proposition that Logic is 
concerned wholly with language is too clear to be 
disputed. 

H— § 16 

The name given to the subject by Aristotle was 
the ** Analytics.^' The name Logic seems to 
have been first applied to it in the time of Zeno, 
the Stoic. Many names have been invented to sig- 
nify the scope of Logic, — as, e. g., the Architectonic 
Art; the Organon, or Instrument; the Ars Artium, 
or Disciplina Disciplinarum; Heuristic, or the Art 

of Discovering TriM; the Medicina Mentis, or the 
16 



242 LOGIC 

Cathartic of the Mind, etc. (Thompson, Laws of 
Thought, §35); ^i^d to these should be added the 
name given by Socrates to his own doctrine (which, 
though the fact is commonly overlooked, was noth- 
ing else than Logic), namely, the Obstetrics of the 
Mind ( Maieusis) , 

Of these, the last two names express precisely 
the two main functions of Logic, — that is to say, 
ist, to serve as a cathartic of the mind to rid it of 
the false persuasion of knowledge; for, as has been 
well said, ** the natural state of the human mind '* 
is ** not simply ignorance, but ignorance mistaking 
itself for knowledge " (Grote's Plato, i., p. 373) ; 
and, 2d, to bring forth from the mind ** answers of 
which it is pregnant" (/^., p. 367); or, in plain 
language, to develop and formulate the unformed 
ideas in our minds, whether innate or acquired 
from without. See Socrates' own account of this 
function, as given in the Theaetetus {Id., iii., p. 
112). 

I— § 37 

There is much confusion with modern logicians 
with regard to the nature of first and second inten- 
tions or notions, but the above definition seems to 
accord with the best authorities and expresses a 
distinction of fundamental importance. According 
to this definition. Notions of Second Intention 
will include all abstract notions, and also notions of 
classes of real individuals construed collectively; 
in which case they become abstract. 

The following is the definition of Aquinas {Opus- 



APPENDIX OF NOTES 243 

cula^ cited Krauth, Voc. of Phil, Art., ** Intention, 
First and Second "): 

** Nouns of first intention are those which are 
imposed upon things as such, that conception alone 
intervening by which the mind is carried imme- 
diately to the thing itself. Such are man and 
stone. But nouns of the second intention are those 
which are imposed upon things not in virtue of 
what they are in themselves, but by virtue of their 
being subject to the intention which the mind 
makes concerning them, as when we say that man 
is a species and animal a genus,'' Which seems to 
accord with our definition : that is to say, if we 
speak of man as denoting the class of individual 
men, the name is of the first intention, but if we 
regard man collectively as a significate of the class 
animal, the name is of second intention; and so 
with reference to all other abstract names. Names 
of second intention are precisely denoted by the 
term '' universale s a parte rei,'' — /. e., universal 
notions considered apart from things, or, in other 
words, abstract notions, — and also by the term 
** beings of reason,'' as quoted infra. 

The division of names into names of first and of 
second intention was obviously intended to com- 
prehend all names; and hence, if names of first 
intention are identical with concrete names, — as they 
evidently are, — names of second intention must in- 
clude all abstract names; and it is not admissible 
to confine them (as Mansel does) to some of that 
class only. Accordingly a universal {ens unum 
in multis) is defined by Aldrich simply as a 



244 LOGIC 

predicable, — i. <?., as ''Nomen Commune^ Univocum^ 
SecundcB Intentionis^ uno verba ^ PredicabiliSy Sive 
Vox apta prcedicare^ i, e, , Univoce did de multis ' * 
(Aid. Log,, p. 23). 

It is singular that in the Port Royal Logic this 
distinction should be regarded as unimportant, and 
even made the subject of ridicule. ** No one, 
thank God! " it is said, " now takes any interest in 
* the universal a parte rei,' or * beings of reason,' or 
in * second intentions.' Thus, there is no ground 
to apprehend that any one will be offended at our 
having said nothing about them." But it may be 
safely said that no one can have an adequate con- 
ception, either of the nature or use of Logic, until 
the notion expressed in the term '* second inten- 
tions," and the other phrases cited (which are 
similar in meaning), are thoroughly grasped. 

K-§38 

Even where we use concrete terms, it is not the 
thing itself, but the notion of the thing that is pres- 
ent to the mind. For, as is said by Hobbes, 
" seeing names ordered in speech (as is defined) 
are signs of our conceptions, it is manifest they are 
not the signs of the things themselves." Hence, 
as Mansel says, ** concepts (or notions^ are the things 
of Logic." On this point Max yi.ySSi^x'^ Laws of 
Thought (the opening chapters) may be read with 
profit. For without acceding altogether to his the- 
ory, — that thought is impossible without language, 
— this is certainly true {ex vi termini), as to ratioci- 
nation, or explicit reasoning, and may therefore be 
accepted without error, and much to his profit, by 



APPENDIX OF NOTES 245 

the logician. According to Home Tooke ** thing ** 
and ''think*' are but the same word spelt differ- 
ently; and hence, he says, ** the vulgar pronuncia- 
tion of ' nothink ' instead of * nothing ' is not so 
very absurd." 

L-§ 53 
bogle's logic 

** All the operations of language, as an instru- 
ment of reasoning, may," it is claimed by Mr. 
Boole, *' be conducted by a system of signs com- 
posed of the following elements," viz. : 

ist. *' Literal symbols, as x, y," etc., represent- 
ing names or terms. 

2d. ** Signs, as +j -", X/* representing relations 
to each other of the substantive elements of com- 
plex terms. 

3d. ** The sign of identity ( = ),'* or, as I should 
call it, the sign of equivalence, /. ^., of significative 
equivalence, or equivalence of denotation. 

The names signified by signs of the first class 
may be either single names denoting classes, — as, 
e, g., man, horse, good, white, etc., — or they may 
be composed of several names, denoting classes 
that partially coincide — as, e. g.^ good men, black 
sheep, etc. In the latter case the signs may be 
combined together precisely as the words denoting 
the terms. Thus, if we represent the class men 
by X, and the class good by y, '* good men " will 
be denoted by the expression yx. So if x stands 
for sheep ^ y for Mach things, and z for horned things , 
zyx will denote *' horned black sheep." But it is 
obvious that in the expression ** black sheep ^'' the 



246 LOGIC 

order in which the component terms are placed 
makes no difference ; or, in other words, that it is 
the same thing whether we say ** black sheep^'' as in 
English, or ** sheep blacky'' as in Spanish and other 
languages. Consequently, the class ** black sheep *' 
may be written either yx or xy^ which may be ex- 
pressed by the following equation: 




(i)yx-xy. X XY Y 



In which the complex term yx or xy denotes a 
class of individuals that is at once included in the 
class _y and the class x. On the same principle, if 
we represent by z the adjective ** horned^'' zyx will 
stand for the term " horned black sheep^'" and we 
will have the following equations: 



(2) zxy = xyz = yxz. 



If, in the equation xy = yx, we suppose y to be 
wholly included in x, — as, e, g., if it denote the 
black sheep in the flock x, — then we will have the 
equation : 




(3) xy = y. 

Again, if x = y, then xy =:x^ But a class is not 




APPENDIX NOTES 247 

enlarged or diminished by repeating the term de- 
noting it. Thus, ** white white " or ''sheep sheep " 
mean nothing more than "white" or ** sheep." 
Hence we have the equation: 

(4) X' = X. 

If the class denoted by a term is composed of 
two classes, denoted respectively by x and y, as, 
e.g.^ *' men and women," it may be expressed by 
the complex term x + y. But obviously, the ex- 
pressions, ** men and women," and " women and 
men," are equivalent in meaning. Hence the 
equation: 

(5) X + y = y + x. 

Again, if we qualify the term ** men and women " 
by the adjective ** Asiatic," we have the expres- 
sion ''Asiatic men and women "; but this is equiv- 
alent in meaning to the expression " Asiatic men 
and Asiatic women." Hence, denoting men by x, 
women by y, and Asiatic by z, we have the equation: 

(6) z(x -f y) = zx + zy. 

If we denote the adult population of a city by x, 
and the women by y, then x — y will denote the 
men. But it is indifferent whether we express the 
excepted class first or last, provided it be distinctly 
represented as the exception. Thus the expres- 
sion, " the adult population less the women," and 
the expression, " excepting the women, the adult 



248 LOGIC 

population," are equivalent in meaning to each 
other, and both to the expression ** the men.'* 
Hence we have the equation: 

(7) X - y = - y + X. 

But the expression, ** the white population, less 
the women,*' is equivalent in meaning to the ex- 
pression, ** the white population, less the white 
women." 

Hence, representing ** white " by z, we have the 
equation: 

(8) z (x — y) = zx — zy. 

If, in the proposition, *' The stars are the suns 
and the planets," we denote stars by x, suns by y, 
and planets by z, we shall have the equation : 

(9) X = y + z. 

But, if the stars are the suns and the planets^ the 
stars^ except \}iq planets^ are suns. Hence we have 
the equation: 

(10) X — z = y. 

If the terms x and y are equivalent, it is obvious 
that those of the class x, or, as we may say, the x's, 
that possess a given quality, must be identical with 
the y's that possess it. Hence, if x = y, we have 
the equation : 

(11) zx = zy. 



APPENDIX NOTES 249 

But, per contra^ it cannot be inferred from the 
equation, zx = zy, that x =r y, (§ 82 (2) n.) 

For, ** suppose it true that those members of a 
class X which possess a certain quality, z, are iden- 
tical with those members of a class y, which possess 
the same quality, z, it does not follow that the 
members of the class x universally are identical 
with the members of the class y/' Thus, return- 
ing to our sheep, let x denote one portion of a 
flock of sheep, and y another, and let z denote 
*' horned'' J then zx will denote the horned sheep 
in one portion of the flock, and zy the horned sheep 
in the other; and, if we suppose these to be equal, 
we shall have the equation: 

zx = zy. 

But it will not follow that the two portions of the 
flock are equal in number, and we therefore can- 
not say X = y ; as may be thus illustrated : 




Adverting to the above equations, it will be per- 
ceived that the laws governing the convertibility of 
the different forms of expression are, to a certain 
extent, identical with those obtaining in mathe- 
matics. Thus, in the equations (i) and (2), the 
symbols are commutative like the symbols of algebra. 
The logical process here involved is, therefore, 
expressed in the same manner as in the correspond- 



250 LOGIC 

ing algebraic expression ; and this expression, 
whether regarded as logical or algebraic, will be 
subject to the same law. There is, therefore, in 
the process involved in these equations, (i) and (2), 
a certain resemblance or analogy to the process of 
multiplication; and this is also true of equation 

(11). 

In equations (6) and (8) a process is exhibited 
closely resembling that of factoring in algebra. 

In equations (5), (7), (9), and (10), we have 
illustrated a principle of conversion of symbols 
apparently identical with the corresponding process 
in algebra. Hence we may affirm as logical axioms: 
ist, that if equals be added to equals the wholes 
will be equal; and, 2d, that if equals be taken from 
equals, the remainders will be equals. 

Hence, with regard to the equations specified 
(i, 2, II, 6, 8, 5, 7, 9, and 10), we may affirm gen- 
erally that the logical symbols may be transposed 
or converted precisely in the same way as in the 
operations of addition, subtraction, and multiplica- 
tion in algebra. But with regard to the analogy 
between multiplication and the corresponding 
logical operation, it will be observed that in one 
respect it fails, namely, in equation (4), x^ = x; 
which is good in Logic, but not generally true in 
algebra. Also, it will be observed, there is appa- 
rently no logical process corresponding to the alge- 
braic operation of division. Thus, as we have 
seen, we cannot infer from equation (n), ** zx = 
zy," that x =: y, as we may in algebra. 

But if we conceive of an algebra or arithmetic 



APPENDIX NOTES 25 I 

that deals only with the two numbers, i and o, this 
discrepancy will altogether disappear. For on such 
hypothesis, equation (4), x^ = x, will be true, both 
in Logic and in mathematics. And in equation 
(11), zx :r= zy, if z == I, the proposition, x = y, 
may be inferred, both in Logic and in mathe- 
matics. But if z be equal to zero, it cannot be 
thus inferred, either in Logic or algebra. Hence, 
if we conceive of an algebra in which the symbols 
x, y, z, etc., *' admit indifferently of the values of 
I and o and of those values alone," then ** the laws, 
the axioms, and the processes of such an algebra 
will be identical in their whole extent with the laws, 
axioms, and process of an algebra of Logic." 

Accordingly, Mr. Boole's system is founded on 
this hypothesis, and ** the logical value and signifi- 
cance " of the terms dealt with (i and o) are thus 
explained. In algebra, the equation oy = o is true, 
whatever the value of y. So, in Logic, if o be re- 
garded as a class, whatever class may be denoted 
by y, the equation oy = o will be true; for, as we 
have seen, oy denotes the class of individuals that 
are at the same time included in the two classes, — 
/. e., o and y. But none are included in the class 
o, and therefore, oy = o. 

So in algebra, the equation ly =: y is true, what- 
ever the value of y may be, and this is true in Logic 
also, if I be regarded as including y. For as we have 
seen (equation 3), if one of the two terms making a 
combined term is included in the other, the com- 
bined term is equal to the term of least extension. 
But this condition may be satisfied by regarding i 



252 LOGIC 

as denoting the Universe. ** Hence, the respective 
interpretations of the symbols, o and i, in the sys- 
tem of Logic, are Nothing and Universe^ Denoting 
the Universe by i, and men by x, the expression 
I— X denotes the class *' not-men,*' — /. e:^ all 
animals that are not men. 

The equation x^ = x may be put in the form, 
x^ — X = o, and this again in the form, x (i — x) 
= o; of which the interpretation is obvious; for, 
if X denotes ** men,*' and i — x *' not-men,*' it is 
clear that there can be no individuals belonging at 
once to the two classes, x and i — x, or, men and 
not-men. So if we denote by x any class charac- 
terized by the possession of any quality whatever 
the same result will follow. 

It is observed by Mr. Boole that the principle of 
analysis and classification involved in his system is 
*' division into pairs of opposites, or, as it is techni- 
cally said, Dichotomy " (§ 47), and this is in fact the 
fundamental process in Logic. And this, it will 
be observed, agrees with the opinion of Hobbes 
and of Aristotle (§ 90 n.). 

In equation (5), it will be observed, there is a 
certain ambiguity in the expression x -f- y. In 
common speech the classes denoted by the sym- 
bols X and y may either be exclusive of each 
other, or they may overlap, as, for instance, in the 
proposition, ** Scholars and men of the world de- 
sire happiness," or, " Useful things are those that 
either produce pleasure, or prevent pain." In 
Mr. Boole's system this ambiguity is removed. 

If the two classes are intended to include each 



APPENDIX NOTES 253 

Other, the expression to denote the aggregate class 
will be X (i — y) + y (i ~ x); which is to be read 
x's that are not y's, and y's that are not x's. 

If we intend two classes that overlap, then the 
full expression should be, xy + x (i— y) + y (i — x). 

** The result of these investigations may be em- 
bodied in the following rule of expression: 

** Rule. — Express simple names or qualities by 
the symbols x, y, z, etc., their contraries by i — x, 
I — z, etc. ; classes of things defined by common 
names or qualities, by connecting the correspond- 
ing symbols as in multiplication; collections of 
things consisting of portions different from each 
other, by connecting the expressions of those por- 
tions by the sign +• Ji^ particular, let the expres- 
sion, * Either x's or y's ' be expressed by x 
(i — y) + y (1 — x) when the classes denoted by 
X and y are exclusive; by x -f y (i — x) when they 
are not exclusive. Similarly let the expression, 
* Either x 's or y's or z's ' be expressed by x 
(i - y) (i - z) + y (i — x) (i - z) + z (i - x) 
(i — y), when the classes denoted by x, y, and 
z are designed to be mutually exclusive; and by 
x + y (i — z )+ z (i — x) (i — y), when they are 
not meant to be exclusive, and so on." 

For illustration, " let us assume 

X = hard, y = elastic, z = metals; 

and we shall have the following results: 

** ' Non-elastic metals ' will be expressed by 

z(i - y); 



254 LOGIC 

'* * Elastic substances with non-elastic metals ' by 
y + z(i - y); 

** * Hard substances, except metals,' by x — y; 

** ' Metallic substances, except those which are 
neither hard nor elastic,' by z — z (i — x) (i — y), 
orbyz[i-(i -x)(i -y)]." 

The above brief account of the elements of Mr. 
Boole's system is given for the purpose of illus- 
trating the laws that govern the convertibility of 
terms, and of substantive elements of terms; or, in 
other words, that govern the formal substitution of 
equivalent expressions, (§ 67 (2)) — a purpose for 
which it admirably serves. It will require some 
attention to understand it, but with such attention, 
no difficulty will present itself. 

It may be readily perceived that by the use of 
the above data a very extensive calculus may be 
developed, and such a one has in fact been devel- 
oped by Mr. Boole; but with regard to its utility, 
opinions may widely differ. 

** The idea of a logical calculus," says Lotze, 
** has been often taken up and often abandoned; 
but the Englishman Boole has recently made an 
elaborate and careful attempt to carry it out, which 
is beginning to attract attention in Germany, as 
well as in his own country. Though I freely 
admit that the author's ingenuity makes his able 
work very charming, I am unable to convince my- 
self that this calculus will help us to solve problems 
which defy the ordinary methods of Logic." 
{Logic ^ vol. ii., 277.) 



APPENDIX NOTES 



255 



M— §96 

TABLE OF SYLLOGISMS 



rYX 

ist Figure \ ZY 

(zx 





Barbara 


A: 


YisX 


A: 


Z is Y (( 


A: 


.'.Z is X 




Celarent 


E: 


Y is not X 


A: 


Zis Y 


E: 


.*. Z is not X 




Darii 


A: 


YisX 


L 


Some Z is Y 


I: 


.*. Some Z is X 







Ferio 


\ E: 


Y is not X 


v) I: 


Some Z is Y 


i) 0:.\ 


Some Z is not X 




(XY 


2d Figure 


■^ZY 




(zx 




Cesare 

X is not Y 

Z is Y 

'. Z is not X 




Celarent 
Y is not X 

Zis Y 

.*. Z is not X 



2s6 



LOGIC 



E: 



A: 



Caniestres 

Xis Y 

Z is not Y 
'. Z is not X 

Festino 

X is not Y 



I: Some Z is 



O: .*. Some Z is not X 



Fakoro 

Xis Y 



O: Some Z is not Y 
O: /. Some Z is not X 



© (0 







Celarent 


E 


Y 


is not Z 


A 


X 


is Y 


E 


.-. X 


is not Z 




or Z 


is not X 




Ferto 






Y 


is not X 



E: 



I: Some Z is Y 

O: .'. Some Z is not X 

Ferio 
E: Not-Y is not X 

I: Some Z is not Y 

O: .*. Some Z is not X 



Darapti 
A: Y is X 

A: Y is Z 

I: .*. Some Z is X 

Disamis 
I: Some Y is X 
A: Y is Z 

I; .*. Some Z is X 



r YX 

^d Figure X YZ 

Izx 







Darii 


A: 


YisX 


I: 


Some Z is Y 


I: 


,*. Some Z is X 




Darii 


A: 


Yis Z 


I: 


Some X is Y 


I: 


.•. Some X is Z 




or Some Z is X 



APPENDIX NOTES 



Datisi 
A: Y is X 

I: Some Y is Z 
I: .'. Some Z is X 

Eelapton 
E: Y is not X 

A: Y is Z 

O: . *. Some Z is not X 

Dokamo 
O: Some Y is not X 
A: Y is Z 

O: .'. Some Z is not X 

Ferison 
E: Y is not X 

I: Some Y is Z 

O: .*. Some Z is not X 







5* 




257 






Darii 




A 


: YisX 




I: 


Some Z is Y 




I: 


.*. Some Z is X 
Ferio 


E: 




Y is not X 


I: 




Some Z is Y 



O: .*. Some Z is not X 



A: 



Darii 



YisZ 



I: Some not — X is Y 

I: .*. Some not — X is Z 

or, Some Z is not — X 

Ferio 
E: Y is not X 

I: Some Z is Y 
O: .*. Some Z is not X 





Bramantip 


A: 


XisY 


A: 


YisZ 


I: 


.-. SomeZ isX 




Camenes 


A: 


Xis Y 


E: 


Y is not Z 


0: 


.*. Z is not X 



/XY 

4th Figure \ YZ 

(zx 




17 




Barbara 

Yis Z 

XisY 

XisZ 

or Some Z is X 



Celarent 

Y is not Z 

X is Y 

.*. X is not Z 

or Z is not X 



258 



LOGIC 





Dimaris 


T: 


Some X is Y 


A: 


Y is Z 


I: 


.*. Some Z is X 




Fesapo 


E: 


X is not Y 


A: 


Yis Z 


I: 


.*. Some Z is not X 




F7'esison 


E: 


X is not Y 


I: 


Some Y is Z 


O: 


. *. Some Z is not X 





Q89 





Darii 




A: Y is Z 




I: Some X is Y 




I: .*. Some X is Z 




or Some Z is X 




Ferio 


E: 


Y is not X 


I: 


Some Z is Y 


O: 


.*. Some Z is not X 




Ferio 


E: 


Y is not X 


I: 


Some Z is Y 


O: 


.'. Some Z is not X 



N— § no 

The opinion of Locke cited, which occurs at the 
end of his essay, may be taken as the consumma- 
tion and final generalization of his theory of knowl- 
edge. In the body of the work the conclusion 
reached by him is, that the elements of all knowl- 
edge are ideas (by which is meant what are now 
commonly called notions or concepts), and that 
** knowledge [is] but the perception of the connec- 
tion and agreement, or disagreement, or repugnancy 
of any of our ideas " ^Essay^ b. 4, c. i). 

This definition, it will be observed, is too nar- 
row, as it excludes the knowledge derived directly 
from the perception of concrete objects. But al- 
lowing for this defect it is accurate and profound 
and must be taken as the foundation of all science. 
In the beginning it seems that Locke had no 



APPENDIX NOTES 259 

conception, or at least a very inadequate conception 
of the intimate connection between language and 
thought, and of the indispensability of the former 
as an instrument of thought. But as he proceeded 
he seems gradually to have realized this great truth, 
— which is treated of in his third book; and upon 
the conclusions thus reached is based his theory of 
knowledge and his general philosophy as developed 
in his fourth book, and as generalized in the conclu- 
ding chapter, to which we have referred. His theory 
of knowledge, therefore, is to be regarded as based 
to a great extent expressly, and otherwise implicitly, 
upon the notion that all knowledge beyond that 
coming from experience consists in the perception 
of the agreement, or disagreement, of our ideas, or 
notions; and hence that all reasoning must consist 
in the comparison of notions or concepts; that 
practically this can be effected only by means of 
the names of the concepts or notions; and hence 
that Logic must consist in Analysis and Synthesis 
of names or terms; which is the theory of this 
work. (See observation of Home Tooke, Appen- 
dix A.) 




INDEX 

Abstract and concrete terms, 37 

Accent, fallacy of, 203 

Accident and genus distinguished, 49 

Accident and secundum quid, relation between, 210 

Accident, fallacy of, 207, 208 

Adjectives regarded as substantives, 36 

Amphiboly, 201 

Analysis and synthesis, logical and physical, distinguished, 108 

Analysis, use of, 116 

Analytical processes, 42 

Apodictic, 23, 70 

Apprehension, 41 

A P7H07H, and empirical notions, 71 

Arguing in circle, 160 

Aristotle, his dictum, 76 ; his classification of fallacies, 197 

Bain, an opinion of, 83 
Burden of proof, 164 



Canons of the several figures of syllogism, 100 
Categories and predicables distinguished, 66 
Classification, division and, 44 
Collective and distributive interpretation, 60 
Commonplace and original thought distinguished, 1 12 
Commonplaces, 156 

The numbers refer to sections. 
261 



262 INDEX 

Common terms, singular and, 35 

Composition and division, fallacy of, 202 

Concept defined, 30 

Concrete terms, abstract and, 37 

Confusion, fallacy of, 139 

Connotation and denotation of terms, 32 

Consequent, fallacy of the, 212 

Consequentis, F., 212 

Contradiction, the law of, 125 

Contradictory, substitution of, 80 

Contraposition, conversion by, 80 

Conversion by intension, 58 

Conversion of propositions, 54, 70, 91 

Conversions, material and formal, distinguished, 92 

Copula, the, 55 

Criticism, 115 

Definition, vocal, 43 ; nominal or real, 48 

Denotation and connotation of terms, 32 

Dialectic, 23, 70 

Dichotomy, 47 

Dictum, Aristotle's, 76 ; forms of, 99 ; applicable to all fig- 
ures, 100, loi ; and to singular and other equational 
propositions, 102 ; proposed amendments of, 103 

Division, 46 

Division and classification, 44 

Enthymemes, 105 

Equational theory of predication, 56 

Equivalence of terms, 78 

Equivocation, fallacy of, 127, 191, 201 

Essence of term, 49 

Euclid, his fifth proposition reduced to syllogisms, 84 

Excluded middle, the law of, 125 

Extension and intension of terms, 34 

The numbers refer to sections. 



INDEX 26^ 

Fallacies, classification of, 129 ; definition of, 128 ; observa- 
tions on, 132 ; extra dictionem, 206 : in dictione (equivo- 
cation), 201; of inference, 131; of judgment, 130; of 
the syllogism, 104, 124 

False definition, fallacy of, 126, 144 

FigurcB dictionis^ F., 204 

Figure of speech, fallacy of, 204 

Figures of the syllogism, 95 

Formal and material conversions, 92 

Formal and material relations of terms, 67 

Formal fallacies, 104 

Genus and accident, 49 
Genus and species, 45 
Genus of term, 49 

Homonymy, 201 

Hypothesis, argument from, 165 n 

Hysteron proteron^ 160 

Identity, the law of, 125 

Ignoratio elenchi, fallacy of, 126, 169 

Illicit assumption of premises {petitio principit)^ 154 ; tests 

of, 162 
Illicit conversions, 127, 183 
Illicit generalization, 155 
Illicit substitution, fallacy of, 127, 187 
Immediate inferences, 80 
Inference, rules of, 77, 123, 127 
Inferences, immediate, 80 
Infinitation, 80 

Instance, or extreme case, 163 
Intension and extension of terms, 34 
Intensive conversion, 58 
Intensive theory of predication, 58 
Intuitive propositions or judgments, 18, 19 

The numbers refer to sections. 



264 INDEX 

Invention, 113 

Irrelevant conclusion, fallacy of, 126, 169, 173 

Judgment, defined, 19 ; rules of, 126 
Judgments and assumptions distinguished, 68 

Knowledge defined, i, 2, 5 

Language, as record of human thought, 4 ; as source of 

opinion, 3 
Laws of thought, the, 125 : the law of identity, 125 ; the 

law of contradiction, 125 ; the law of excluded middle, 

125 

Legal maxims, 158 

Logic, definition of, 14, 16 ; the traditional, 85 ; decadence 
of the age in, 11 ; method of, iii ; the morality of in- 
tellect, 27 ; the art of right reasoning, 26 ; the ultimate 
criterion of truth, 10 ; as the doctrine of signs, no 

J^ogical processes, 107, 112 

Logical term, elements of the, 31 

Material and formal conversions, 92 
Material and formal relations of terms, 67 
Mathematical reasoning, 82 
Meaning and signification of terms, 33 
Method of logic, in 
Mistaking the issue, 169, 170 
Moods of the syllogism, 94 

Moral sciences, distinguished, 6 ; decadence of the age in the, 
II 

Name defined, 28 

Negative terms, positive and, 39 

Nominal or real definition, 48 

Non causa pro causa, fallacy of, 159 

Nonsense, fallacy of, 126, 134, 138 

Notion defined, 30 

The numbers refer to sections. 



INDEX 265 

Onus probandiy 164 

Opinion, its modes of generation, 7 ; language as source of, 3 

Opposition of propositions, 89 

Original and commonplace thought distinguished, 112 

Petitio principii^ fallacy of, 126 

Plurium inter rogationuni^ F., 171 

Popular proverbs, 157 

Positive and negative terms, 39 

Post hoc ergo propter hoc^ 159 

Predicables, definition and division of, 61 ; and categories dis- 
tinguished, 66 

Predication, theories of, 55, 60 

Property and specific difference distinguished, 49 

Proposition, defined, 22, 50; the grammatical, 51; the logi- 
cal, 52 ; interpretation of the logical, 53 ; the traditional 
doctrine of the, 86 

Propositions, conversions of, 54, 91 ; kinds of : intuitive, 18, 
20 ; quasi-intuitive, 20 ; inferred, 21 

Proverbs, popular, 157 



Quality of propositions, 86 
Quantification of the predicate, 57 
Quantity of propositions, 87 
Quasi-thing defined, 29 
Question-begging terms, 161 



Ratiocination, defined, 14, 15 ; not merely hypothetical, 72 

Real things defined, 29 

Reasoning, defined, 14 ; supposed distinction between quali- 
tative and quantitative, 82 

Reductio, ad absurdum^ 165 ; ad impossibile^ 165 n 

Reduction of syllogisms, 96 

Relations of terms, immediate ; intuitive relations or judg- 
ments, 18, 19 ; quasi-intuitive, or assumptions, 20 ; in- 
ferred relations or syllogisms, 21 

The numbers refer to sections. 



266 INDEX 

Right reasoning defined, 25 

Rules, of logic, twofold division of, 121 ; of inference, 77, 
123, 127 ; of judgment, 122, 126 ; of the syllogism, 104 

Secundum quid, fallacy of, 209 

Semeiotike, or the doctrine of signs, no 

Several questions, fallacy of, 171 

Significates of terms, 33 

Signification and meaning of terms, 33 

Simple apprehension, 41 

Singular and common terms, 35 

Sorites, 106 

Species, genus and, 45 

Specific difference, 49 

Substitution, the principle of, 77 ; formal and material, 81 ; 
of contradictory, 80 

Syllogism, analysis of, 74 ; definition of, 22, 75 ; elements of, 
73 ; moods and figures of, 94, 95 ; principle of, 76 ; re- 
duction of, 96 ; rules of, 104 ; the traditional doctrine of, 
93 

Term, defined, 28 ; Mnds of, 35 

Terminal relations, generally, 64 ; kinds of, 17, 65 

Tests of illicit assumption, 162 

Thing defined, 29 

Thought defined, 30 

Traditional doctrine of fallacies, 197 

Traditional theory of predication, 59 

Universe of the proposition, 40 

Vocal definition, 43 

Word defined, 28 

The numbers refer to sections. 








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